, y= g(x )'
a) Ve do thi (P) cua ham so y= va diTdng thing (D):y =-x 1 tren ciing mot he true tpa dp.
mot he true tpa dp.
b) T i m tpa dp c^c giao diem cua (P) va (D) bang phep tinh.
Bai 3: (1,5 diem) Tinh (rut g p n ) : * ' '
A = ^/l2-6^/3 + V2I-I2V3
B = 5
\
^ a i 4: (1,5 diem) Cho phirdng trinh x^ - (3m + l)x + 2m^ + m - I = 0 (x la an so). .ChiJng minh rang phirdng trinh luon luon c6 hai nghiem phan bỉt vdi moi
gia tri cua m.
b) Goi X|, X2 la cdc nghiem cua phufdng trinh. Tim m de bieu thiJc sau dat gia tri Idn nhaft: A = xf + - 3 x i X 2 .
Bai 5: (3,5 diem) Cho duTdng tron tarn O difdng kinh AB = 2R. Goi M la mot diem bat ki thuoc dUdng tron (O) khac A va B. Cac tic'p tuyen cua (O) tai A va M c^t nhau tai Ẹ Ve MP vuong goc vdi AB (P thuoc AB), ve MQ vuong
gdc vdi AE (Q thupc AE).
a) Chu-ng minh rkng AEMO la tuT giac npi tiep diTdng tron va APMQ la hinh chff nhat.
b) Goi I la trung diem cua PQ. Chtfng minh O, I, E thing hang.
c) Goi K la giao diem cua EB va MP. ChiJng minh hai tarn giac EAO va MPB dong dang. Suy ra K la trung diem cua MP.
d) Dat AP = X. Tinh MP theo R va x. Tim vi tri cua M tren (O) de hinh chu" nhat APMQ c6 dipn tich Idn nhát.
Hl/CfNG DAN GIA I Bat l:a)2x^ - 3 x - 2 = 0, A = 9+ 16 = 25, 7A = 5.
J_
2" 3 "f" 5 3 5 PhiTdng trinh c6 hai nghiem phan biet: X| = = 2 ; X2 = —-— b) 4x + y = -1 f8x + 2y = -2 <=> < 6x - 2y = 9 [6x - 2y = 9 14x = 7 6x - 2y - 9 <=> i 1 X = — 2 6 . - - 2 y = 9 2 <=> < 1 X = - 2 « < -2y = 6 X = — 2 . c) 4x'' - 13x^ + 3 = 0. Dat y = x^ (y > 0)
PhiTdng trinh trd thanh 4y^ - 13y + 3 = 0, A = 169 - 48 = 121, VA = 11. 13 + 11 ^ 13-11 1 , . . , y, = — - — = 3 (nhan); yi = — - — = - (nhan) • y, = 3 ta c6 x^ = 3 <=>x = ±V3. • y2 = - ta c6 x^ = - o x = ±-. 4 4 2 V a y S= { V 3 ; - ^ ; ^ ; - ^ } d) 2x^-2>/2x - 1 = 0,Á = 2 + 2 = 4, VÁ = 2.
PhUdng trinh c6 hai nghiem phan biet: X| = ^ ^ ; X2 = ——-.
Cty TNHH MTV DWH Khang Vi$t
Nhan xet: a ) , d) Giai phiTdng trinh ax^ + bx + c = 0 (a 0) b k n g c o n g thtfc n g h i e m . b ) Hay g i a i h e p h i T d n g t r i n h nay bhng phufdng p h a p t h e . • .
c ) Dat x^ = y d e diTa v e g i a i phu-cfng t r i n h b a c h a i 4y^ - I3y + 3 = 0.
Co t h e g i a i triTc t i e p : 4x' - 13x' + 3 = 0 <=> 4x' - x' - 12x' + 3 = 0
C: > x W - D - 3(4x'- l) = 0<:^(4x'- IXx^ _ 3) = Q Bai 2: a) Bang gia tri : Bai 2: a) Bang gia tri :
Do thj h a m so":
b) Phifdng trinh hoanh do giao diem cua (P) va (D): - y = - X - 1 <:^-x' = X- 2 <=> x^ + X - 2 = 0 o X = 1 hoac X = -2 (vi CO a + b + c = 1 + 1 - 2 = 0) 1^ 1 • X = 1 thi y = -— = - i ^ 2 2 • x = - 2 t h i y = -^_±l-=_2. X -4 -2 0 2 -4 • • ' " »•' X 0 2 -x^ y= 2 -8 -2 0 -2 -8 y= ^ x - 1 -1 0
Vay (D) va (P) cift nhau tai hai diem 1 ; - - 2,
va (-2 ; -2).
Nhan xet : Cac nghiem cua phifdng trinh hoanh do giao diem cua (P) va (D)
^ 1 ,
— — = - X - 1 la Cclc hoanh do cua cac giao diem. Bai 3:
^) A = + V 2 I - I 2 V 3 = V(3 - V3)' + V(273 - 3 ) '
= 3 - 73| + I2V3 - 3|= 3 - V3 + 2 V3 - 3 = N/3
( V i 3 - V3 >Ova 2V3 - 3 > 0 ) B = 5
= 5