ࡱ>  DZ~P| N X M C ~ bjbjSS 411VbJJJJJ^^^8:$L^@%X3XXXXs $0J=mJ|s=JJXX<###FJXJX###wX^9/w0\,:,0,J#==#, : CHUYN  BI DNG HC SINH GII LNG GIC PHN 1 Gii phng trnh:  EMBED Equation.DSMT4 \* MERGEFORMAT  Hng dn gii iu kin:  EMBED Equation.DSMT4  (*). Vi iu kin trn, phng trnh  cho tng ng:  EMBED Equation.DSMT4 \* MERGEFORMAT   EMBED Equation.DSMT4 \* MERGEFORMAT   EMBED Equation.3 \* MERGEFORMAT   EMBED Equation.3 \* MERGEFORMAT  TH1:  EMBED Equation.DSMT4 \* MERGEFORMAT  TH2:  EMBED Equation.3 \* MERGEFORMAT   EMBED Equation.3 \* MERGEFORMAT  i chiu iu kin ta thy phng trnh  cho c 2 h nghim  EMBED Equation.DSMT4 \* MERGEFORMAT . Tm tt c cc nghim x EMBED Equation.DSMT4 (2009; 2011) ca phng trnh :  EMBED Equation.DSMT4  Chng minh rng:  EMBED Equation.DSMT4  Cho:  EMBED Equation.DSMT4 , vi  EMBED Equation.DSMT4 . Chng minh rng:  EMBED Equation.DSMT4 . Gii phng trnh :  EMBED Equation.DSMT4  Cho tam gic  EMBED Equation.DSMT4  vi cc k hiu thng thng, bit:  EMBED Equation.DSMT4  Chng minh rng tam gic  EMBED Equation.DSMT4  cn. Gii phng trnh sau:  EMBED Equation.DSMT4  Tm a  bt phng trnh ng vi mi x:  EMBED Equation.DSMT4  Cho tam gic  EMBED Equation.DSMT4  c  di cc cnh l  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 ,  di ba ng phn gic trong tng ng vi cc gc  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4  ln lt l l EMBED Equation.DSMT4 , l EMBED Equation.DSMT4 , l EMBED Equation.DSMT4 . 1. Chng minh rng:  EMBED Equation.DSMT4  2. Nhn dng tam gic, bit:  EMBED Equation.DSMT4  nh a  h:  EMBED Equation.DSMT4  c nghim duy nht. Chng minh rng nu  EMBED Equation.DSMT4  th:  EMBED Equation.DSMT4  Tm  EMBED Equation.DSMT4   h phng trnh sau y c nghim v hy gii h phng trnh tng ng vi nhng gi tr tm c ca m:  EMBED Equation.DSMT4  Cho hai phng trnh sau:  EMBED Equation.DSMT4  (1)  EMBED Equation.DSMT4  (2) a. Gii cc phng trnh trn vi  EMBED Equation.DSMT4 . b. Tm tt c cc gi tr ca  EMBED Equation.DSMT4   hai phng trnh (1) v (2) tng ng. Gii h phng trnh:  EMBED Equation.DSMT4  Tm tt c cc gi tr  EMBED Equation.DSMT4  sao cho:  EMBED Equation.DSMT4  Tm s t nhin  EMBED Equation.DSMT4  nh nht  phng trnh sau c nghim:  EMBED Equation.DSMT4  Cho tam gic  EMBED Equation.DSMT4  c  EMBED Equation.DSMT4 . Chng minh rng:  EMBED Equation.DSMT4  Cho tam gic  EMBED Equation.DSMT4  c  di ba cnh tho mn h thc:  EMBED Equation.DSMT4  Tnh tng s o gc:  EMBED Equation.DSMT4  Xt cc tam gic  EMBED Equation.DSMT4  tho mn rng buc:  EMBED Equation.DSMT4 . Tm gi tr ln ca biu thc:  EMBED Equation.DSMT4  Tm m  phng trnh sau c nghim:  EMBED Equation.DSMT4  Chng minh rng vi mi  EMBED Equation.DSMT4  ta lun c  EMBED Equation.DSMT4 . Tm tt c cc gi tr ca tham s m  phng trnh sau c nghim  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4 . Tm tng nghch o cc nghim ca phng trnh  EMBED Equation.DSMT4  tha mn iu kin  EMBED Equation.DSMT4  Tm m  phng trnh  EMBED Equation.DSMT4  c ng 8 nghim trn khong  EMBED Equation.DSMT4  Trong tt c cc tam gic  EMBED Equation.DSMT4  cho trc, tm tam gic c  EMBED Equation.DSMT4  ln nht. Gii phng trnh :  EMBED Equation.DSMT4  Tnh s o cc gc trong tam gic  EMBED Equation.DSMT4  , bit  EMBED Equation.DSMT4  Gii phng trnh EMBED Equation.DSMT4  Tam gic  EMBED Equation.DSMT4  tha mn ng thc EMBED Equation.DSMT4  Tm s t nhin a b nht  phng trnh sau c nghim :  EMBED Equation.3  Cho tam gic  EMBED Equation.DSMT4  c : tanA+tanC=2tanB.CMR :  EMBED Equation.3  Gii phng trnh:  EMBED Equation.DSMT4  Trong tam gic  EMBED Equation.DSMT4  bit s o ba gc  EMBED Equation.DSMT4  lp thnh cp s cng vi  EMBED Equation.DSMT4  v tha h thc  EMBED Equation.DSMT4 . Tnh s o cc gc  EMBED Equation.DSMT4 . Gii phng trnh  EMBED Equation.DSMT4  Tm m  phng trnh sau c 4 nghim phn bit trong khong  EMBED Equation.DSMT4 :  EMBED Equation.DSMT4  Gii phng trnh : cosx.cos2x = 1/4 Hng dn gii x=k khng phi l nghim.nhn thm sinx vo hai v  a v pt sin4x=sinx Suy ra x=k2/3 ; x=/5 +k2/5 v x`"k nn pt c cc nghim x=2/3 +k2; x=/5 +k2; x=3/5 +k2 Gii phng trnh:  EMBED Equation.DSMT4  Cho phng trnh:  EMBED Equation.DSMT4  a) Gii phng trnh khi  EMBED Equation.DSMT4 . b) Xc nh tham s  EMBED Equation.DSMT4   phng trnh c ng mt nghim  EMBED Equation.DSMT4 . Cho tam gic  EMBED Equation.DSMT4  c cc gc A, B, C tha mn h thc:  EMBED Equation.DSMT4  Chng minh tam gic  EMBED Equation.DSMT4  l tam gic u. Gii phng trnh :  EMBED Equation.DSMT4 . Tm m  phng trnh cos EMBED Equation.3  c nghim. Tam gic  EMBED Equation.DSMT4  c ba gc tha mn h thc :  EMBED Equation.3 . Hy tnh cc gc ca tam gic . Gii phng trnh:  EMBED Equation.DSMT4  Gii phng trnh sau  EMBED Equation.DSMT4 . Hng dn gii  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Vy phng trnh c hai h nghim:  EMBED Equation.DSMT4  Cho  EMBED Equation.DSMT4  vi  EMBED Equation.DSMT4 . Tnh gi tr ca biu thc:  EMBED Equation.DSMT4  Hng dn gii Do  EMBED Equation.DSMT4  nn  EMBED Equation.DSMT4 . Ta c:  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4  Khi :  EMBED Equation.DSMT4  Tm tp xc nh ca hm s  EMBED Equation.DSMT4  Hng dn gii ieu kien xac nh  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Tm gi tr nh nht ca hm s  EMBED Equation.DSMT4  Hng dn gii *  EMBED Equation.DSMT4  *  EMBED Equation.DSMT4  *  EMBED Equation.DSMT4  GTNN y = 1 * y = 1  EMBED Equation.DSMT4  Gii phng trnh  EMBED Equation.DSMT4  Hng dn gii  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Tm tt c gi tr thc  EMBED Equation.DSMT4   phng trnh sau c hai nghim phn bit thuc  EMBED Equation.DSMT4 :  EMBED Equation.DSMT4  Hng dn gii * t = cotx ,  EMBED Equation.DSMT4  *  EMBED Equation.DSMT4  (1)  EMBED Equation.DSMT4  (2) Pt(1) c 2 nghim phn bit  EMBED Equation.DSMT4  EMBED Equation.DSMT4 pt(2) c 2 nghim dng phn bit  EMBED Equation.DSMT4   EMBED Equation.DSMT4 ket qua ung : m < - 1 v 0 < m<  EMBED Equation.DSMT4  Gii phng trnh  EMBED Equation.DSMT4  Hng dn gii Tp xc nh: D = R. Phng trnh  cho tng ng vi phng trnh:  EMBED Equation.DSMT4  Xt hm s f(t) =  EMBED Equation.DSMT4 , ta c f(t) ng bin vi mi t nn ta c: f(3cosx) = f(4cos3x) ( 3cosx = 4cos3x ( cos3x = 0 ( x =  EMBED Equation.DSMT4 , k ( Z Tm m  bt phng trnh sau ng vi mi x. (1 + 2cosx(+ (1 + sin2x(( 2m  1 Hng dn gii t f(x) = (1 + 2cosx( + (1 + 2sinx(. Bi ton tr thnh: tm m sao cho maxf(x) ( 2m  1. Ta c f2(x) = 6 + 4(sinx + cosx) + 2(1 + 2(sinx + cosx) + 4sinxcosx( t t = sinx + cosx,  EMBED Equation.DSMT4 . Ta c: f2(x) = g(t) = 6 + 4t + 2(2t2 + 2t  1( vi  EMBED Equation.DSMT4 . Xt s bin thin ca g(t) ta c:  EMBED Equation.DSMT4  V f(x) ( 0 nn ta c: maxf(x) =  EMBED Equation.DSMT4  Vy ta c:  EMBED Equation.DSMT4 . Rt gn tng S =  EMBED Equation.DSMT4  trong  n l mt s t nhin. Bit rng sin2x + sin2y =  EMBED Equation.DSMT4 , tm gi tr ln nht v gi tr nh nht ca S = tg2x + tg2y. Rt gn : P =  EMBED Equation.DSMT4 . Chng minh rng nu ta c  EMBED Equation.DSMT4  th  EMBED Equation.DSMT4 . Trong tam gic  EMBED Equation.DSMT4  c A = 360, AB = AC = 1 v BC = x. Gi s  EMBED Equation.DSMT4 , hy tm cp s nguyn (p, q). Cho  EMBED Equation.DSMT4 . Chng minh rng:  EMBED Equation.DSMT4 , (a > 0, b > 0). Cho  EMBED Equation.DSMT4 . Tnh gi tr ca biu thc  EMBED Equation.DSMT4  Tnh gi tr ca biu thc:  EMBED Equation.DSMT4 . Cho tam gic  EMBED Equation.DSMT4  bt k. Tm c im ca tam gic khi biu thc  EMBED Equation.DSMT4  t gi tr ln nht. Cho cc s thc a, b, c tho mn  EMBED Equation.DSMT4 . Tm gi tr ln nht v gi tr nh nht ca biu thc  EMBED Equation.DSMT4 , trong   EMBED Equation.DSMT4 . Tm gi tr ln nht ca hm s  EMBED Equation.DSMT4  vi  EMBED Equation.DSMT4 . Tm gi tr nh nht ca hm s EMBED Equation.DSMT4 vi n l s t nhin. Cho tam gic  EMBED Equation.DSMT4  tho mn: 2tgB = tgA + tgC. Chng minh rng: a) B EMBED Equation.DSMT4 , b) cosA+ cosC  EMBED Equation.DSMT4 . Cho tam gic  EMBED Equation.DSMT4  tho mn:  EMBED Equation.DSMT4 . Chng minh rng iu kin cn v   tam gic  EMBED Equation.DSMT4  vung l  EMBED Equation.DSMT4 . Tnh tng S =  EMBED Equation.DSMT4 . Chng minh rng:  EMBED Equation.DSMT4 . Cho x, y, z, t l cc s thc nm gia EMBED Equation.DSMT4 v EMBED Equation.DSMT4  tho mn:  EMBED Equation.DSMT4 . Chng minh rng: 0 EMBED Equation.DSMT4 x, y, z, t  EMBED Equation.DSMT4 . Tm GTNN ca hm s  EMBED Equation.DSMT4 . Tm GTNN, GTLN ca hm s:  EMBED Equation.DSMT4 . Tm GTLN, GTNN ca hm s:  EMBED Equation.DSMT4 . Cho tam gic  EMBED Equation.DSMT4  c C = 2B = 4A. Gi O, H ln lt l tm ng trn ngoi tip, trc tm ca tam gic  EMBED Equation.DSMT4 . Tnh t s  EMBED Equation.DSMT4 trong  R l bn knh ng trn ngoi tip tam gic. Cho tam gic  EMBED Equation.DSMT4  vung  C. Gi r l bn knh ng trn ni tip tam gic,  EMBED Equation.DSMT4 ln lt l  di cc ng trung tuyn ca tam gic k t A, B. Tm gi tr ln nht ca:  EMBED Equation.DSMT4 . Gii cc phng trnh sau: 1/  EMBED Equation.DSMT4 . 2/  EMBED Equation.DSMT4 . 3/  EMBED Equation.DSMT4 . 4/  EMBED Equation.DSMT4  5/  EMBED Equation.DSMT4 . 6/  EMBED Equation.DSMT4  Chng minh rng: 4cos36 EMBED Equation.DSMT4  EMBED Equation.DSMT4  Cho  EMBED Equation.DSMT4 . Tnh  EMBED Equation.DSMT4 . Chng minh rng:  EMBED Equation.DSMT4 . Thu gn tng S = EMBED Equation.DSMT4 . Thu gn P = (2cosa-1)(2cos2a-1)... EMBED Equation.DSMT4  Tnh cc tng: S = EMBED Equation.DSMT4 , P =  EMBED Equation.DSMT4 , R =  EMBED Equation.DSMT4  Gi M v m l gi tr ln nht v nh nht ca hm s F(x)=cos(2006x)+kcos(x EMBED Equation.DSMT4  trong  k, EMBED Equation.DSMT4  l cc tham s thc. Chng minh rng: EMBED Equation.DSMT4  Hy xc nh dng ca tam gic  EMBED Equation.DSMT4  nu cc gc ca tam gic  EMBED Equation.DSMT4  tho mn ng thc sau:  EMBED Equation.DSMT4  PHN 2 Gii cc phng trnh sau y: EMBED Equation.DSMT4  Hng dn gii: Ta c:  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4 . Gii cc phng trnh lng gic sau: a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4  Hng dn gii: a)  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  iu kin:  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Vi  EMBED Equation.DSMT4 , khng tha mn iu kin Vi  EMBED Equation.DSMT4  Gi tr  EMBED Equation.DSMT4  b loi do iu kin  EMBED Equation.DSMT4  Vy pt  cho c h nghim l:  EMBED Equation.DSMT4  c)  EMBED Equation.DSMT4   EMBED Equation.DSMT4 . Gii phng trnh  EMBED Equation.DSMT4 . Hng dn gii  EMBED Equation.DSMT4  khng phi l nghim.nhn thm  EMBED Equation.DSMT4  vo hai v  a v pt  EMBED Equation.DSMT4 . Suy ra  EMBED Equation.DSMT4 ;  EMBED Equation.DSMT4 . V  EMBED Equation.DSMT4  nn pt c cc nghim  EMBED Equation.DSMT4 ;  EMBED Equation.DSMT4 ;  EMBED Equation.DSMT4 . Gii phng trnh  EMBED Equation.DSMT4 . Hng dn gii  EMBED Equation.DSMT4 . Theo BT Bunhiacpski  EMBED Equation.DSMT4 . Vy phng trnh xy ra khi v ch khi  EMBED Equation.DSMT4 (H phng trnh v nghim). Vy phng trnh  cho v nghim. Tm nghim dng nh nht ca phng trnh  EMBED Equation.DSMT4 . Hng dn gii  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Ta c:  EMBED Equation.DSMT4 (nghim dng nh nht khi  EMBED Equation.DSMT4 ). (2) c  EMBED Equation.DSMT4 (do  EMBED Equation.DSMT4  nguyn). (2) c hai nghim  EMBED Equation.DSMT4 . Suy ra nghim dng  EMBED Equation.DSMT4  nh nht khi  EMBED Equation.DSMT4 . Khi   EMBED Equation.DSMT4  Vy nghim dng nh nht ca pt l  EMBED Equation.DSMT4 . Cho phng trnh: EMBED Equation.DSMT4 . a. Gii phng trnh khi EMBED Equation.DSMT4 . b. Tm m  phng trnh c nghim  EMBED Equation.DSMT4 . Hng dn gii a. khi  EMBED Equation.DSMT4  phng trnh  EMBED Equation.3 .  EMBED Equation.DSMT4 . b. Tm m  phng trnh c nghim  EMBED Equation.DSMT4 . phng trnh  EMBED Equation.3 . vi  EMBED Equation.DSMT4  ta c  EMBED Equation.3  nn  EMBED Equation.DSMT4  khng tho mn. Do  phng trnh  cho c nghim  EMBED Equation.DSMT4  EMBED Equation.DSMT4 . Tm nghim ca phng trnh EMBED Equation.3  tha mn iu kin:  EMBED Equation.DSMT4 . Hng dn gii  EMBED Equation.3 (*) +  EMBED Equation.3   EMBED Equation.DSMT4  + EMBED Equation.DSMT4   EMBED Equation.DSMT4  hoc  EMBED Equation.DSMT4  +  EMBED Equation.DSMT4 (1) +  EMBED Equation.DSMT4  (v  EMBED Equation.DSMT4  khng th xy ra) Ta c: EMBED Equation.DSMT4  hoc  EMBED Equation.DSMT4  EMBED Equation.DSMT4 . + Vi iu kin  EMBED Equation.DSMT4 , chn s nguyn  EMBED Equation.DSMT4 . Vy  EMBED Equation.DSMT4 . Cho phng trnh  EMBED Equation.DSMT4  (1) ( EMBED Equation.DSMT4  l tham s). a. Gii phng trnh (1) vi  EMBED Equation.DSMT4 . b. Tm  EMBED Equation.DSMT4   phng trnh c nghim. Hng dn gii a. Vi  EMBED Equation.DSMT4 . Thay vo phng trnh  EMBED Equation.DSMT4  ta c:  EMBED Equation.DSMT4 . b. Phng trnh c nghim  EMBED Equation.DSMT4 . Gii phng trnh:  EMBED Equation.DSMT4  Hng dn gii iu kin:  EMBED Equation.DSMT4 . Ta c:  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 . Vy phng trnh c h nghim l  EMBED Equation.DSMT4  v  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 . Cho phng trnh  EMBED Equation.DSMT4 . Tm cc gi tr ca  EMBED Equation.DSMT4  sao cho phng trnh  cho c nghim. Li gii KX:  EMBED Equation.DSMT4 . Vi iu kin  chia hai v ca phng trnh cho  EMBED Equation.DSMT4 , ta c:  EMBED Equation.DSMT4  t  EMBED Equation.DSMT4 , ta c phng trnh:  EMBED Equation.DSMT4  Do phng trnh  EMBED Equation.DSMT4 c nghim vi mi  EMBED Equation.DSMT4  nn phng trnh  cho c nghim khi v ch khi  EMBED Equation.DSMT4  c nghim  EMBED Equation.DSMT4 . Gii phng trnh  EMBED Equation.DSMT4  Li gii KX:  EMBED Equation.DSMT4 . Ta c:  EMBED Equation.DSMT4   EMBED Equation.DSMT4 . Gii phng trnh  EMBED Equation.DSMT4  Li gii iu kin:  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 . Gii phng trnh  EMBED Equation.DSMT4  Li gii  EMBED Equation.DSMT4   EMBED Equation.DSMT4 . Gii phng trnh  EMBED Equation.DSMT4  Li gii  EMBED Equation.DSMT4  EMBED Equation.DSMT4  (iu kin:  EMBED Equation.DSMT4 )  EMBED Equation.DSMT4 . Tm iu kin ca tham s  EMBED Equation.DSMT4   phng trnh  EMBED Equation.DSMT4  c nghim. Li gii t  EMBED Equation.DSMT4 , iu kin  EMBED Equation.DSMT4 . Phng trnh  EMBED Equation.DSMT4  (1) tr thnh  EMBED Equation.DSMT4  (2).  (1) c nghim th (2) phi c nghim  EMBED Equation.DSMT4 . Lp bng bin thin ca  EMBED Equation.DSMT4 , da vo bng bin thin ta c iu kin cn tm l  EMBED Equation.DSMT4 . Vi gi tr no ca  EMBED Equation.DSMT4  th phng trnh  EMBED Equation.DSMT4  c nghim? Li gii  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Phng trnh c nghim  EMBED Equation.DSMT4 . Cho 3 s thc EMBED Equation.DSMT4 . S nghim ca phng trnh  EMBED Equation.DSMT4  trn khong  EMBED Equation.DSMT4  l A.  EMBED Equation.DSMT4 . B.  EMBED Equation.DSMT4 . C.  EMBED Equation.DSMT4 . D. thay i theo  EMBED Equation.DSMT4 . 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lng gic, cc h nghim ca phng trnh  EMBED Equation.DSMT4  s c biu din bi 2 im i xng vi nhau qua  EMBED Equation.DSMT4 , m  y  bi ch cho trn 1 gc phn t th IV nn ch c 1 nghim duy nht. Vi gi tr no ca  EMBED Equation.DSMT4  th phng trnh  EMBED Equation.DSMT4  c nghim Li gii Ta c:  EMBED Equation.DSMT4   EMBED Equation.DSMT4 . Phng trnh c nghim khi  EMBED Equation.DSMT4 . Gi  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4  l gi tr ln nht v gi tr nh nht ca hm s  EMBED Equation.DSMT4 . Li gii t  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 . Ta c  EMBED Equation.DSMT4   EMBED Equation.DSMT4 . Ta c hm s  EMBED Equation.DSMT4 . Bng bin thin:  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 Suy ra  EMBED Equation.DSMT4 . Tm tt c cc gi tr ca tham s  EMBED Equation.DSMT4   phng trnh  EMBED Equation.DSMT4  v nghim. Li gii  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 . Phng trnh v nghim  EMBED Equation.DSMT4  EMBED Equation.DSMT4 . Tm tt c cc gi tr ca tham s  EMBED Equation.DSMT4   phng trnh  EMBED Equation.DSMT4  c nghim  EMBED Equation.DSMT4 . Li gii  EMBED Equation.DSMT4  khng l nghim ca phng trnh. t  EMBED Equation.DSMT4   EMBED Equation.DSMT4 . Ta c phng trnh  EMBED Equation.DSMT4  EMBED Equation.DSMT4 . Phng trnh c nghim  EMBED Equation.DSMT4  EMBED Equation.DSMT4  c nghim  EMBED Equation.DSMT4 . Phng trnh  EMBED Equation.DSMT4  l phng trnh honh  giao im parabol  EMBED Equation.DSMT4  v ng thng  EMBED Equation.DSMT4 . Bng bin thin ca hm s  EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 Da vo bng bin thin, phng trnh  EMBED Equation.DSMT4  c nghim  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 . Phng trnh  EMBED Equation.DSMT4  c bao nhiu nghim dng b hn  EMBED Equation.DSMT4 ? Li gii  EMBED Equation.DSMT4  EMBED Equation.DSMT4 . Ta c:  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 . Du  EMBED Equation.DSMT4  xy ra  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4 Vy c  EMBED Equation.DSMT4  nghim dng b hn  EMBED Equation.DSMT4  ng vi  EMBED Equation.DSMT4 . Biu din tp nghim ca phng trnh  EMBED Equation.DSMT4  trn ng trn lng gic ta c bao nhiu im? Li gii iu kin:  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 . + Vi  EMBED Equation.DSMT4  (khng tha iu kin). + Vi  EMBED Equation.DSMT4 (tha iu kin). Biu din hai h nghim  EMBED Equation.DSMT4  trn ng trn lng gic ta c  EMBED Equation.DSMT4  im. PHN 3 Gii cc phng trnh sau:  EMBED Equation.DSMT4  Hng dn gii. iu kin:  EMBED Equation.DSMT4  Phng trnh  cho tng ng vi:  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 . i chiu iu kin ta c nghim ca phng trnh l  EMBED Equation.DSMT4 ( EMBED Equation.DSMT4 ). Gii cc phng trnh sau:  EMBED Equation.DSMT4  Hng dn gii. Phng trnh  cho tng ng vi  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4  Gii phng trnh  EMBED Equation.DSMT4  Hng dn gii. Phng trnh  cho tng ng vi  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 . Gii phng trnh:  EMBED Equation.DSMT4 . Hng dn gii. iu kin:  EMBED Equation.DSMT4  ( nu th sinh vit khng  (*) th tr 0,5 im). Khi :  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 . Kt hp vi iu kin (*) ta c nghim ca phng trnh l  EMBED Equation.DSMT4 . Cho phng trnh:  EMBED Equation.DSMT4  ( m l tham s). Gii phng trnh khi  EMBED Equation.DSMT4 . Tm  EMBED Equation.DSMT4   phng trnh sau c bn nghim phn bit thuc on  EMBED Equation.DSMT4 . Hng dn gii. Phng trnh  cho tng ng vi:  EMBED Equation.DSMT4  (  EMBED Equation.DSMT4  (1). Vi  EMBED Equation.DSMT4  ta c phng trnh:  EMBED Equation.DSMT4  2) t t = cos4x ta c:  EMBED Equation.DSMT4 , (2). Vi  EMBED Equation.DSMT4  th  EMBED Equation.DSMT4  Phng trnh (1) c  EMBED Equation.DSMT4  nghim phn bit  EMBED Equation.DSMT4  khi v ch khi phng trnh (2) c  EMBED Equation.DSMT4  nghim phn bit  EMBED Equation.DSMT4  (3). Xt g(t) =  EMBED Equation.DSMT4  vi  EMBED Equation.DSMT4  ta c bng bin thin: t  EMBED Equation.DSMT4   EMBED Equation.DSMT4  1 g(t)  5 3  EMBED Equation.DSMT4  Da vo bng bin thin suy ra (3) xy ra (  EMBED Equation.DSMT4 (  EMBED Equation.DSMT4  Vy gi tr m cn tm l:  EMBED Equation.DSMT4 . Gii phng trnh: 2sinx.(1 + cos2x) + sin2x = 1+ 2cosx. Hng dn gii Ta c PT  EMBED Equation.3  (2cosx + 1).(sin2x  1) = 0 . p s:  EMBED Equation.DSMT4 . Tnh cc gc ca tam gic ABC, bit rng  EMBED Equation.DSMT4 . Hng dn gii ng thc  EMBED Equation.3   EMBED Equation.3 . p s: A = C = 300 ; B = 1200. Gii phng trnh :  EMBED Equation.DSMT4 . Hng dn gii  EMBED Equation.DSMT4  .  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4  . Gii phng trnh: 2sin x +  EMBED Equation.DSMT4  = 0. Hng dn gii 2sin x +  EMBED Equation.DSMT4  = 0  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 . Gii phng trnh:  EMBED Equation.DSMT4 . Hng dn gii  EMBED Equation.DSMT4 . iu kin :  EMBED Equation.DSMT4 . PT  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 . t :  EMBED Equation.DSMT4 . Ta c:  EMBED Equation.DSMT4 . Vi  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4  . Hng dn gii Xt phng trnh:  EMBED Equation.DSMT4  (1). iu kin:  EMBED Equation.DSMT4 . Phng trnh (1)  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4   EMBED Equation.DSMT4 .  EMBED Equation.DSMT4  EMBED Equation.DSMT4 . i chiu vi iu kin:  EMBED Equation.DSMT4 . Vy phng trnh c nghim:  EMBED Equation.DSMT4 . Gii h:  EMBED Equation.DSMT4 . Hng dn gii iu kin:  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 , ta c  EMBED Equation.DSMT4  v  EMBED Equation.DSMT4 . Kt hp vi  EMBED Equation.DSMT4  ta c:  EMBED Equation.DSMT4 . Cng  EMBED Equation.DSMT4  v  EMBED Equation.DSMT4  ta c EMBED Equation.DSMT4 , th vo  EMBED Equation.DSMT4  ta c:  EMBED Equation.DSMT4  t  EMBED Equation.DSMT4 , phng trnh  EMBED Equation.DSMT4  tr thnh  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 . Vi  EMBED Equation.DSMT4 , ta c  EMBED Equation.DSMT4 . Vy h phng trnh c  EMBED Equation.DSMT4  nghim  EMBED Equation.DSMT4  l  EMBED Equation.DSMT4  v  EMBED Equation.DSMT4 . Gii cc phng trnh sau:  EMBED Equation.DSMT4 . Cho phng trnh: EMBED Equation.DSMT4 . a) Gii phng trnh vi  EMBED Equation.DSMT4 . b) Tm  EMBED Equation.DSMT4   phng trnh c nghim thuc [0; EMBED Equation.3 ]. Tnh cc gc ca tam gic  EMBED Equation.DSMT4  bit:  EMBED Equation.DSMT4 . Gii phng trnh:  EMBED Equation.DSMT4 . Tm gi tr nh nht ca hm s:  EMBED Equation.DSMT4 . Cho s thc x tha mn  EMBED Equation.DSMT4 . Tnh gi tr biu thc  EMBED Equation.DSMT4 . Gii phng trnh  EMBED Equation.DSMT4 . PHN 4 Gii phng trnh sau:  EMBED Equation.DSMT4  Hng dn gii iu kin:  EMBED Equation.DSMT4  (*). Vi iu kin trn phng trnh  cho tng ng vi:  EMBED Equation.DSMT4  Kt hp vi iu kin (*) ta c nghim ca phng trnh  cho l:  EMBED Equation.DSMT4  v  EMBED Equation.DSMT4  . Gii phng trnh:  EMBED Equation.DSMT4 . Hng dn gii iu kin:  EMBED Equation.DSMT4  (*). Vi iu kin trn phng trnh  cho tng ng vi:  EMBED Equation.DSMT4  Kt hp vi iu kin (*) ta c nghim ca phng trnh  cho l:  EMBED Equation.DSMT4  Gii phng trnh: EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.3  Gii phng trnh:  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4  Cho hm s:  EMBED Equation.DSMT4  Gii phng trnh: a)  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  Chng minh vi mi gi tr ca  EMBED Equation.DSMT4 ta c:  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4  Cho phng trnh sau:  EMBED Equation.DSMT4  a) Gii phng trnh khi  EMBED Equation.DSMT4   EMBED Equation.DSMT4  b) Xc nh tham s  EMBED Equation.DSMT4   phng trnh c ng 1 nghim . Cho phng trnh sau:  EMBED Equation.DSMT4  (vi  EMBED Equation.DSMT4 l tham s). a) Khi  EMBED Equation.DSMT4 , hy tm tt c cc nghim  EMBED Equation.DSMT4  ca phng trnh. b) Xc nh  EMBED Equation.DSMT4   phng trnh c nghim  EMBED Equation.DSMT4 . Tm  EMBED Equation.DSMT4  thuc khong  EMBED Equation.DSMT4  nghim ng phng trnh:  EMBED Equation.DSMT4  . Gii phng trnh:  EMBED Equation.DSMT4 . Gii phng trnh:  EMBED Equation.DSMT4 . Cho phng trnh:  EMBED Equation.DSMT4  Tm  EMBED Equation.DSMT4   phng trnh c ng 4 nghim thuc  EMBED Equation.DSMT4  . Cho  EMBED Equation.DSMT4  Chng minh rng:  EMBED Equation.DSMT4 . Chng minh rng:  EMBED Equation.DSMT4 . Gii phng trnh:  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4 . Gii phng trnh:  EMBED Equation.DSMT4 . Tm  EMBED Equation.DSMT4   phng trnh:  EMBED Equation.DSMT4  c nghim  EMBED Equation.DSMT4  v ch c nghim y. Gii phng trnh:  EMBED Equation.DSMT4 . Gii phng trnh:  EMBED Equation.DSMT4 . Gii phng trnh:  EMBED Equation.DSMT4 . Cho phng trnh:  EMBED Equation.DSMT4  Tm  EMBED Equation.DSMT4   phng trnh c nghim. Tnh tng cc nghim ca phng trnh:  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4  Gii phng trnh sau:  EMBED Equation.DSMT4  Gii phng trnh sau:  EMBED Equation.DSMT4 . Gii phng trnh:  EMBED Equation.DSMT4  Hng dn gii  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4  Hng dn gii K  EMBED Equation.DSMT4  Khi  phng trnh  cho tr thnh  EMBED Equation.DSMT4   EMBED Equation.DSMT4  +)  EMBED Equation.DSMT4  khng tha mn K +)  EMBED Equation.DSMT4  (tha mn K)  EMBED Equation.DSMT4  Gii cc phng trnh sau y:  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4  Hng dn gii +) iu kin +) Tm c tanx = 1 hoc tanx = 0 +) Gii ng v loi nghim ng. S:  EMBED Equation.DSMT4  Tm m phng trnh:  EMBED Equation.DSMT4  c nghim  EMBED Equation.DSMT4  Hng dn gii +) a PT v dng:  EMBED Equation.DSMT4  (1) +) t t = cos4x vi  EMBED Equation.DSMT4  EMBED Equation.DSMT4 t EMBED Equation.DSMT4 (-1; 0) +) Xt f(t) = 2t2 + t trn (-1; 0) c bng bin thin V PT (1) c nghim khi ng thng y = 2m +1 (song song hoc trng 0x )ct f(t) trn (-1; 0) +) S:  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4  Gii phng trnh:  QUOTE   Hng dn gii Dng cng thc h bc ta c:  QUOTE    QUOTE   S dng ct nhn i gii c: sinx=0; sinx=1/2 T  suy ra nghim ca pt:  QUOTE   Gii phng tnh :  EMBED Equation.DSMT4  Cho hm s  EMBED Equation.DSMT4 . Tm gi tr ln nht v nh nht ca hm s trn EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.3  Gii phng trnh:   EMBED Equation.DSMT4  Hng dn gii Ta c:  EMBED Equation.DSMT4   EMBED Equation.DSMT4  t:  EMBED Equation.DSMT4  Ta c:  EMBED Equation.DSMT4  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Cho phng trnh sau:  INCLUDEPICTURE "http://www.thuvienkhoahoc.com/dethi/images/math/3128d91f17ab73529e758a0be89930d6.png" \* MERGEFORMATINET  vi m l tham s. 1) Khi m = 0, hy tm tt c cc nghim  INCLUDEPICTURE "http://www.thuvienkhoahoc.com/dethi/images/math/0459000be143035777b17e74fb2ae472.png" \* MERGEFORMATINET ca phng trnh. 2) Xc nh m  phng trnh c nghim  INCLUDEPICTURE "http://www.thuvienkhoahoc.com/dethi/images/math/7e66cfb694860da93ab64d3936e8da34.png" \* MERGEFORMATINET  Cho phng trnh sau:  INCLUDEPICTURE "http://www.thuvienkhoahoc.com/dethi/images/math/bcbe1abae624d93a65c723d09072b9e7.png" \* MERGEFORMATINET  1) Gii phng trnh khi  INCLUDEPICTURE "http://www.thuvienkhoahoc.com/dethi/images/math/af9dc81ad51d1c9c6c1b7abd50c5c684.png" \* MERGEFORMATINET . 2) Xc nh tham s m  phng trnh c ng mt nghim  INCLUDEPICTURE "http://www.thuvienkhoahoc.com/dethi/images/math/94d74b0a121e4ab4de22b68b726833ef.png" \* MERGEFORMATINET  Gii phng trnh:  EMBED Equation.DSMT4  Tnh gn ng cc nghim (, pht, giy) ca phng trnh  EMBED Equation.DSMT4 . Hng dn gii Bin i phng trnh  EMBED Equation.DSMT4  Do phng trnh c 3 h nghim l  EMBED Equation.DSMT4  Cho tam giac ABC Co goc A,B nhon thoa ieu kien :  EMBED Equation.3  .Chng minh tam giac ABC vuong Hng dn gii T gt co SinA(SinA-CosB) +SinB(SinB-CosA)=0 EMBED Equation.3 (1) (2) La#i co :  EMBED Equation.3 (2) (2) V#y SinA=CosB ho#c SinB=CosB  EMBED Equation.3  Tam giac a cho vung i nh C (1) Gii phng trnh:  EMBED Equation.DSMT4  Gii phng trnh: 1) Sin  EMBED Equation.3  sinx - cos  EMBED Equation.3 . sin2x + 1 = 2 cos2 EMBED Equation.3  2) 2 cos EMBED Equation.3  Gii phng trnh : 3tan2x -  EMBED Equation.3  = 0 Gii phng trnh:  EMBED Equation.DSMT4  Hng dn gii  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4  Hng dn gii KX:  EMBED Equation.DSMT4 . Phng trnh  cho tng ng  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  hoc  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  Kim tra K tha mn. Vy nghim ca PT l  EMBED Equation.DSMT4  Tm s t nhin a b nht  phng trnh sau c nghim.  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.DSMT4  Gii phng trnh:  EMBED Equation.3  Gii phng trnh:  EMBED Equation.3  Hng dn gii  EMBED Equation.3   EMBED Equation.3  Gii (1) ta c x=k EMBED Equation.3 vi k EMBED Equation.3  Gii (2): Ta c (2)  EMBED Equation.3  EMBED Equation.3   EMBED Equation.3  (3) p dng BT Csi cho 3 s:  EMBED Equation.3 ta c :  EMBED Equation.3  EMBED Equation.3   EMBED Equation.3 . Do  EMBED Equation.3 < EMBED Equation.3  Suy ra (3) v nghim nn (2) v nghim. Kt lun: Phng trnh c nghim x=k EMBED Equation.3 vi k EMBED Equation.3  Gii phng trnh:  EMBED Equation.DSMT4  Hng dn gii PT  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4  +)  EMBED Equation.DSMT4   EMBED Equation.DSMT4 . +)  EMBED Equation.DSMT4 . 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