V id song song vdi canh BC nc nd nhan B C= (1; 3) lam vcctd
3.(1,0diem) Giai hat phiTi/ng trinh
N / X' - 2X- 8 < 6 - (X- 4 ) (X + 2 )O \ / X- - 2X- 8 + X- - 2X- 1 4 < ( ) ( * ) Dal u = N/X- - 2 X -8, U > 0 X - -2X = U - + 8 Dal u = N/X- - 2 X -8, U > 0 X - -2X = U - + 8
(*) ihanh u + u" - 6 < 0 o u" + u - 6 < 0 <=> -3 < u < 2.
Kel hịfp vdi dieu kicn u > 0 la c6 0 < u < 2. Do do:
\ < - 2 [-^ x - - 2 x - 8 > ( ) [-^ x - - 2 x - 8 > ( ) ()< Vx--2x ~8 <2 ^ <=> X -1 - < X < -2x -12 <() -2 4 < x < l + Vil3 X >4 1 - x/l3 < X < 1 + N/I3 l(\Q
Vay lap nghicm ciia BPT T = ( l - y i 3 ; -2\<j\4; \ 0,25
II
(1,5 diem) diem)
1. (0.75 diem) Tim k de hC' bat phifofng trinh sau co n^hi^m...
II (1,5 (1,5 diem) 2 x - 5 > - 4 x + 31 (1) Xct he: < . [x- - ( k + l)x + k < ( ) (2)
Ta CO (!)<=> X > 6. Vay lap hdp nghicm ciia (1) la S = [6; + oo).
PhiMng irinh x^ - ( k + l)x + k = 0co hai nghicm la 1 vii k.
0,25
II
(1,5 diem) diem)
. k = 1: (2) irc) lhanh x^ - 2x + 1 < 0 <=> (x - 1)^ < 0 <=> x = 1. Dc lháy trong Iri/iing help nay he v6 nghicm. Dc lháy trong Iri/iing help nay he v6 nghicm.
• k < 1:(2) CO lap nghicm la doan |k ; 1). Khi do Irong trifdng h(tp nay he v6 nghicm. h(tp nay he v6 nghicm.
0,25
II
(1,5 diem) diem)
• k > 1: (2) CO lap nghicm la doan 11 ; k]. Khi do he co nghicm khi k> 6. V a y he bál phifdng Irinh da cho co nghicm khi khi k> 6. V a y he bál phifdng Irinh da cho co nghicm khi
k >6.
0,25
II
(1,5 diem) diem)
2. (0,75 diem) Tim ni de bát phifc/ng trinh sau v6 nghicm
II (1,5 (1,5 diem) Dal l ' ( x ) - ( m - 3 ) x - -(2m + l)x + m + 2 r(x) > 0 vo nghicm khi f(x) < 0, Vx e K. 0,25 II (1,5 diem)
• m 3 : Khi do < 0 <=> x > (khong ihoa man). 0,25
II (1,5 (1,5 diem) . m ^ 3: Khi do r(x) < 0, Vx e 1 o J ""^ ^ ^ [ A < O [ m < 3 [ m < 3 [(2m+ 1)^ - 4 ( m - 3 ) ( m + 2 ) < 0 [8m + 2 5 < 0 25 25 <=> m < Viiy l(x) > 0 v6 nghiem khi m <
X 8
0,25
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