Question

Решите уравнение (x-1)(x-2)=(3x+2)(3-x)+2

Answer 1

Ответ:

$x = frac{1}{2} ; 3$

Объяснение:

$(x - 1) (x - 2) = (3x + 2) (3 - x) + 2$

$x^{2} - 3x + 2 = (3x + 2) (3 - x) + 2$

$x^{2} - 3x + 2 = 7x - 3x^{2} +8$

$4x^{2} - 10x + 2 = 8$

$4x^{2} - 10x + 2 - 8 = 0$

$4x^{2} - 10x - 6 = 0$

$2 (2x + 1) (x - 3) = 0$

$(2x + 1) (x - 3) = 0$

$2x + 1 = 0$

$2x = -1$

$x = -frac{1}{2}$

$x - 3 = 0$

$x = 3$

$x = frac{1}{2} ; 3$

Ответ: $x = frac{1}{2} ; 3$