. Tru hai phuong trinh ciia h^ ta dugc: ,,
Phuong trinh tro thanh:
^(x-l)(x-2)(2x-3)=0<::>x = l,x = 2,x = -
Vi 2: G i i i cac phvromg trinh sau:
a) V7x + 7+V7x-6+2V49x2+7x-42 =181-14x b) 5Vx+ ^ — ^ = 2x + — + 4 b) 5Vx+ ^ — ^ = 2x + — + 4 2Vx 2x c) x 3 . i l - x ^ ) =x/2(l-x^) GiAi: a) Dieuki^n: x^ỵ Dlt t = V7x + 7+V7x-6,(t>0)=>14x + 2V49x2+7x-42 = 1 ^ - 1 BPT da cho tro thanh:
t + t 2 - l = 1 8 1 « t 2 + t - 1 8 2 = 0 o t = 13
t = -14 <:>t = 13
o V 7 x + 7+V7x-6=13 n
Vi ham so £(x) = V7x + 7 + V7x-6 -13 la ham dong bien va f(6) = 0 Ket hop voi dieu ki^n suy ra nghi^m aia phuong trinh la x = 6. Ket hop voi dieu ki^n suy ra nghi^m aia phuong trinh la x = 6.
1 ^ = 2 x + - = 2 x + -
x + i = t 2 - l .
4x b) Dieu ki^n: x > 0. Phuong trinh <=> 5 b) Dieu ki^n: x > 0. Phuong trinh <=> 5
Datt = 7^ + ^ , f t > 7 2 2Vx ^ ' 2Vx ^ '
Phuong trinh tro thanh:
5t = 2 ( t 2 - l ) + 4 < » 2 t 2 - 5 t + 2 = 0 o t = 2 <::>x + - ^ = 3 3-2>/2 3-2>/2
4x + 4
<»4x^ -12x + l = 0 o x = •
X = • 3+2V2 la nghi^m cua puong trinh.
c) Dieu ki^n: -1 < x < 1. Phuong trinh da cho tuong duong voi x + Vl-x^ Y x ^ - x V l - x ^ +l-x^l = x72(l-x^) x + Vl-x^ Y x ^ - x V l - x ^ +l-x^l = x72(l-x^)
Dat t = X + Vl-x^ => = xVl-x^ . Ta c6 phuong trinh:
Cty TNHHMTVDWHKhartgVm ( J. ( J. 1- t ^ - 1 2 t = V ^ = — « t^ + V2t2 - 3t - N/2 = 0 « (t - N/2 )(t2 + 2^/2t +1) = 0 •t = ^/2 t = - V 2 ± l t2+2V^t + l = 0 + Neu: t = N/2 ^ x + Vl-x^ =V 2 « 7 2 - X = N/I-X2 » ( V 2 - X ) =l-x2(do|x|<l) <s>2x^-2>/2x + l = 0<=>x = ^ + Neu t = -V2 -1 <=> X + Vl-x^ = -1 - >/2 v6 nghỉm ,do VT > -1 > VP + Neu t = -N/2+l»\/rV =l->/2-x -1<X<1-N/2 _ _ I _ V ^ _ 7 2 V 2 - 1 x 2 - ( l - 7 2 ) x - 7 2 + l = 0 o X =
Vay phuong trmh co 2 nghi^m x = — ; x = ^