3(6x^2-x)^2-4(6x^2-x)+1=0

Question

3(6x^2-x)^2-4(6x^2-x)+1=0

Answer 1

3(6х^2 - х)^2 - 4(6х^2 - х) + 1 = 0
Замена: 6х^2 - х = t
3t^2 - 4t + 1 = 0
(t - 1)(3t - 1) = 0
t1 = 1 ; t2 = 1/3

6x^2 - x = 1 или 6х^2 - х = 1/3 |*3
6x^2 - x - 1 = 0 или 18х^2 - 3х - 1 = 0
D = (-1)^2 - 4*6*(-1) ; D = (-3)^2 - 4*18*(-1)
D = 25 = 5^2 ; D = 81 = 9^2
x1 = 1 + 5 / 12 ; x2 = 1 - 5 / 12 ; x3 = 3 + 9 / 36 ; x4 = 3 - 9 / 36
x1 = 1/2 ; x2 = -1/3 ; x3 = 1/3 ; x4 = -1/6

Ответ: 1/2 ; -1/3 ; 1/3 ; -1/6

Answer 2

6x^2-x=y, 3y^2-4y+1=0, y1=1, y2=1/3,
6x^2-x-1=0, x1=1/2, x2=-1/3,
6x^2-x-1/3=0, x3=1/3, x4=-1/6;