EE THI MON: TOAN KIIOI A, B
CAU N( )I DT]NG D I-1 (tei6m) Ydi m= 1 ta cd y = xt -6x' +9x-1. * Tflp xdc dinh: D = R x Su bidn thiOn . Chidu-bidn thi€n: !'=3x2 -l2x+9:3(x2 -4x+3) [x>3
Tac6 _y'>0<+l Lx.,t, _y'<0<+1< x<3.
Do d6:
+ Him sd ddng bidn tr€n m6i khoAng (-*,1) vd (3, + oo)
+ Hdm sd nghich bidn trOn khoing(1, 3).
0,25
0,25
. crlc tri: Him sd dat cuc dai tai x=7 vd !co=y(1):3; dat cuc tidu tai x=3 vd
!ct. = /(3) : -l .
o Gi6i nan:
"l]\/ - -co; 1im y - +a.
o Biing bidn thiOn:
0,25
0,25 * Dd thi:
}lA rhi .3t frrrn frrnd toi fiid*rsrr6 rllr ulvltl (0, -l).
t-2
(ldi6m)
Him sd dat cuc dai, cuc tidu tai xt, x2 <+ phuong trinh y,= 0 c6 hai nghi€m pb li x,, x, <+ R x2 -21m+l)x+3=0 c5hainghiOmphdnbi6t ld x1, x2. <+ A'- (m +1)2- 3 > 0 ol*> -t + '6 lm<-t-Ji (l) 0,25 0,25 0,25 0,25 +) Theo dinh lf Viet ta c6 x, + x, :2(m +1); xrxr: 3. Khi d6
1", -"rl - 2 e (x, + xr)' - 4*r*, - 4 e a(m +l)' -lz : 4
^ f m:-3
e (m +l)' :1o | (2)
Lm=l
II-1(1 di6m) (1 di6m)
PT e 1+3cosr+cos 2x-2cos(2x+x) = 4sinx.sin2r
<+ 1 + 3cosx+ cos 2x -2(cosx.cos2x -sinx.sin 2x) = 4sin x.sin2x 4,2:0,2: 0,2:
<> I + 3 cosx + cos 2x -2(cos.r.cos2x+ sin x.sin 2x) = 0
<+ 1 +3cosx+ cos 2x -2cosr = 0 <+ I + cos.r+ cos 2x = 0
e 2costx+cosx=0 [cosx = o = o ol l I cosx = -; 0,2 0,2 [": * l": 7r -+Klr2 *?o *y2, J tt-z (l iliem) [*' *2x+ y2 t y :3- xy e[*t * xy + y2 +2x+y = 3 (1)
lxy + x+2y :I l*y * * *2y =l (2)CQng (1) vn (2) theo vti dugc (*+ y)' +3(x+ y)-4 =0 CQng (1) vn (2) theo vti dugc (*+ y)' +3(x+ y)-4 =0
0,2 0,2 0,2 0,2 Suy ra fx+y=1 l**r=u
V6i x+ y:l thay vno (2) dugc -y2 *2y =g
Iip {y".:(py)-: (l;o} (x;y)
=
(:l; 2)
V6i x+ ! = -4 thay vdo (2) duqc -y2 -3y-5 :0
Phuong trinh vd nghiQm
Hq c6 2 nghiQm (x;y): (l;0); (x;y): (-l;2)
ilI
(1 di6m)
0,2
0,2
-Jil"otI*t r cotx*l-ra(cotx) 0,2:
0,2: Ji (-*t r+ h lcot x + rl)+C IV (1 tti6m) Do AH L(A,B.C,) nOn g6c AAIH bang 300.
4H li g6c gifra AA, vi (A,B,C,), theo gii thidt thi g5c
{\//
/ ".. 'i/ /
=/y",
X6t tam gi6c vuOng AHA' c6 AA' = a, g6c 4H =30" =+ AH :I a a2 Jt o"li I a a2 Jt o"li AtBtc 3 z 4 24 I 2 V ur"nrurr, : ! dn 's
X6t tam gi6c vuOng AHAr c6 AA, = a, g6c AAtH=300 =+ AtH :+ Do tam gi6c AlBlCr lI tam gi6c ddu canh a, H thudc B,C, vlL AlH =
{ ^r^A,H vuong g6c vdi B,C,.
MAtkhfc AH LB,C, nOn BtCt L(AA.H)
0,25
Ta c6 AAT.HK = ATH.AH + HK = AtH '!H = oJi
Mt42 2 Tucrng tg c6: I-bc> 1-ca) , (r *").,(r *oXr*a) (r *r)u(r+"[r+a) 2 1r *a;n(r *"1r *"; b2 r'ra,
[r.:)(r.;)[r.:) -[r.#)' = o' Do d6 min p : 8 d4t clusc khi a : b : c
_lJ J V
(1 ili6m)
Ggi giao di6m tht hai cria duong thing cdn tim vdi (Cr) vi (Cz) ldn luqt li M vd N Ggi M(x; V)e (C,) + x2 + y2 :13 (l)
Vi A h trung di6m ctra MN n€n N(4 - x; 6 - y). Do N e (Cr)
= (2+ x)2 +(6- y)2 =25 (2)
ouc"e itrins ;a; ti- aiq; A ;t M a6 ph;o"s tiintr : i - at + i : 0
Tri (l ) vd (2) ta c6 hQ ' {*' * v' ^=13
f(z* x)z +(6-!)2 :25
ciei hetadusc (x:2; y: 3) (lo4i vi trungA) vdC :# t r:: ). Vay*f
{ t !l
VI- 1(l tli6m) (l tli6m)
\ \ \ YT-2 (1 di6m) AC : 3J2 suy ra BA: BC : 3 l{*-s>' +(y -3)' +(z +t)' =9 1@-z)' +(y-3)' +(z+4)' =9 I L"*, -z-6:0 0,2: 0,2 0,2 0,2 lf*-s>'+(y-3)' +(z+t\' :9 l{*-s)' +(4-2x)2 +(2-x)2 :s <+jx+z-l:O o|t=l-x L"*y - z -6:0 ll =7 -2x
Tim dusc: 8(2;3;-1) hoac B(3;1;-2)
vII.
(1rti6m)
Dk:x)0,x+3,*+!
9 0,2:
0,2:
Q -toerx)logr*, - *fu - | 4a (z- tog,.)G;- jr* =,
2 -los" x 4
aJ "' - -1
D{t: t:log3x ptthinh,?-.4 =1, h+1't *-z ft =-l
2+t t-t *lt' -3t-4-geLi :o' 0,2So siinh diAu kiQn duoc 2 nghiQm I x =81 So siinh diAu kiQn duoc 2 nghiQm I x =81
J 0,2