,.S.1*Uil'- : VrY ?4^^^
oAp AN DqT 4 (tom t6t) Cdu Ị t)Ydim:0ta c6y - 13-3n2 + ý :3:r2-6r,ý:0 <+ n:0,n:2vd.lirn,-*4*g: toọ Hdm s6 đng bi6n tr€n c5c kho6,ng (-*;0),(2;*m) vh nghlch bi6n tr€n kho6ng (0,2) Tir d6
rCD : IrUco : 0i xcr : 2rACr : -4.
2) Ta c6 u : (* - *) ("'* 3r * m) (C*) c6t Ox tai 3 di6m phdn biQt khi vb chi khi e (r) : 12 -SrIm: 0 c6 2 nghiQm ph6,n bi€t kh6c m e A : 9-4m > 0 vh, s @) : m2 -2m * 0 + m < 914
vir m I 0,m * 2 (*) Khi d6 9 (r) c6 hai nghi€m 11 1 n2 N6u rn < 0 vb th6a m6n (x) theo dinh
lf viet suy ra !11n2. '0+ y:0 c6 hai nghiQm 6m (rn,,11) vb, mQt nghiQm drtong lr2 (loq,i) N6u
m) 0 vb, th6a md,n (*) theo dfnh If viet suy ra n1,t2 ) 0 =+ y: 0 c6 ba nghiQm duong (th6a
man).Vgy0<m<914,m12.
CAu IỊ 1) Dk 1 1r 13 Phuong trinh d5, cho trrong duong vdi 16 1â/l-r - 1:
Bxz - 4r - + o ffiv + #- : (n -2) (3r + 2) e (r - 4 (#n - 6+i - 3r -r) : ọ
Bi6u thfc trong ngof,c td hbm nghich bi6n vd, gi6 tr! tqi c : 1 lb -5 n6n n6 nhQ,n gi6 tri 6,m vdi rngi 1 < r ( 3 Do d6 phrrong trinh c6 nghiQm duy nh6t r: 2 (th6a mdn).
2) Phrrong trinh d5, cho trtoug drrong v6i 4sinrcosrcos2r * cos3c * cosr :4sinn *2
e 2sinr (cos 3r * cosr) * cos 3r * cos r : 4sinr * 2
<+ (2sinr* 1) (cos3o * cosr -2):0 <+ sinr : -ll2 ho{,c cos3r: cosn = 1
# r : -n 16 * k2r;n : 7n/6 * k2n;r : kzn (k e Z)
cdu rrr l) Ta c6 1 : -' ("'-t)a" p (t-1')á
' ắ+*) L
f ffi : I T+f : IE# : -j=,+" : -;h+c (c tb hhng s6)
2) Gqi,4:"s5 drrgc chgn khdng c6 chrl s6 1rr, B:r's6 drrgc chgn khOng c6 chfr s6 5'' Ta cAn
tinh P (A u B) Ta c6 P (A u B) : P (A) + P (B) - P (An B) 56 c5,c trudng hqp c6 th6 khi chqn mOt s6 c6 5 chrl s6 ll 9.t04.
56 trudng hgp thugn lgi cho 4 ti 8.94 (v) c5,c chrl s6 khdc 1 n€n chrl s6 đu ti6n c6 8 c5.ch
chqn (kh6,c I vd, khac 0), 4 chrl s6 ti6p theo m6i s6 c6 9 c6,ch chgn (vi kh6c 1)), tuong tU s6
trrJdns hop thu6n IOi cho B Ie 8.94, 56 tnrdng hgp thuQn lgi cho An B }} 7.84' VQ.y ta c6
P (AuB) : z aug:1:i aa
CAu pitago) IV 1) \ gB : CA: DB : DA: a,AB : art ncn frB :TiE: 90" (theo dinh $
=+ 6CE : 668 : 90' ( theo dinh lf ba drrdng vudng g6c) + B H ld dudng kinh duong trbn ngopi ti6p tam gi5,c d6u BCD =+ BH:"2* * AHz: AB2 - BHz:2"'- *:* *
AH : e*.ydy vẹBcno: *SacnọAH : +."?+ + : o"#.
2) Gqi P(np,aild6i xftng M(4,6)qua I thi 1 Ib, trung di6m MP
"c" {1
*,
" : ?:' , , thuQc rl t6 *so :2u\ á
ncn {1p - 5(6tvP) +6 : 0 nen 3r p -5yp-6 : 0 (1) Ta lai c6 P M r PN suy ra M P.N P : 0
hay(rp-4@p-o)+(sp-6)(ap-2):0 (2).Tt(1),(2)tathudttgcS4y2r-t62yp*180:0
<lod6go:3 ho6,c up:30ll7.Khigr:3thi np:7 phrlongtrinh cD i x:-a -4:0, khi
yp :30117 thi tung dO I nh6 hdn 4 n€n ioat:-.
3) Ta c6 1(1,1, 1) lir trung diiSm AB, khi d6 lM A+ MEI : 2MI b6 nh6t khi M II hinh chi6u cria
l lOn (p) phrrongtrinhdrrbngthS.ng dquaf vu6ngg6c (P)Id,d: a:l*7t, U:t+\t, z:t+t
th6vb,ophrrongtrinh(P) tac67(l+7t)+5(1+5t)+1+t+62:0vQ,yt:-1 tatimdrrgc M(*6, -4,0)
Cdu V Ta-chrlng minh k6t qu5 t6ng qu6t sau: v6i t,u,'.))rn)n,p,r,A, z ) 0 ta c6 tt"u + +Ftne +
VW < (**) That v6'Y, theo bdt C6-si
t;/ -1
-
< t + u + =+,- Vi6t hai bAt d8.ng thfc trrdng tU rdi
oll (t+n+tw+nIv)@+p+z) : t+n+e ' u*nla ' ưp+z
l6y tiing ciị ba ta thu drrqc 3VT(*'r)lVP(**) < 3 suy ía (**) tiiing Ap dr.rng n5t aing thrlc nd,y
vdi t: rm: .x : l;u: a,tu : b,A : ciu : llb,p : llc,z : Llạ Ta c6 ngay didu ph6'i chrlng
minh D6u bH,ng xAY ra khi a : b = c: L.
T -co 0 2 *o<
Íb\ + 0- 0 +
t@)
,/\,/
,/\/