Найдите корни уравнений:a) (2x-1)(x-2)=-1b) 23-x=(x-3)²c) -8x²-5x+7=(1-2x)²d) x-5√x+6=0

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a) (2x-1)(x-2) = -1
2x^2 - 4x - x + 2 = -1
2x^2 - 5x + 2 + 1 = 0
2x^2 - 5x + 3 = 0
(2x - 3)(x - 1) = 0
2x - 3 = 0 => x = 3/2
x - 1 = 0 => x = 1

b) 23 - x = (x - 3)^2
23 - x = x^2 - 6x + 9
x^2 - 7x + 9 - 23 = 0
x^2 - 7x - 14 = 0
(x - 14)(x + 1) = 0
x - 14 = 0 => x = 14
x + 1 = 0 => x = -1

c) -8x^2 - 5x + 7 = (1 - 2x)^2
-8x^2 - 5x + 7 = 1 - 4x + 4x^2
-8x^2 - 5x + 7 = 1 - 4x + 4x^2
-8x^2 - 5x + 7 = 4x^2 - 4x + 1
12x^2 - x + 6 = 0
(4x - 3)(3x - 2) = 0
4x - 3 = 0 => x = 3/4
3x - 2 = 0 => x = 2/3

d) x - 5√x + 6 = 0
Let y = √x
y^2 - 5y + 6 = 0
(y - 2)(y - 3) = 0
y - 2 = 0 => y = 2
y - 3 = 0 => y = 3
√x = 2 => x = 4
√x = 3 => x = 9

Корни уравнений:
a) x = 3/2, x = 1
b) x = 14, x = -1
c) x = 3/4, x = 2/3
d) x = 4, x = 9