Question

Решите уравнение пожалуйста,даю 30 баллов.
(х-2)²=(7-2х)²​

Answer 1

$x {}^{2} - 4x + 4 = 49 - 28x + 4x {}^{2} \\ x {}^{2} - 4x + 4 - 49 + 28x - 4x {}^{2} = 0 \\ - 3x {}^{2} + 24x - 45 = 0 \\ x {}^{2} - 8x + 15 = 0 \\ x = \frac{ - ( - 8) + - \sqrt{ (- 8 ){}^{2} - 4 \times 1 \times 15 } }{2 \times 1} \\ x = \frac{8 + - \sqrt{64 - 60} }{2} \\ x = \frac{8 + - \sqrt{4} }{2} \\ x1 = \frac{8 + 2}{2} = 5 \\ x2 = \frac{8 - 2}{2} = 3$

Answer 2

Решение:

(х - 2)² = (7 - 2х)²​

x² - 4x + 4 = 49 - 28x + 4x²

x² - 4x + 4 - 49 + 28x - 4x² = 0

-3x² + 24x - 45 = 0 | : (-3)

x² - 8x + 15 = 0

D = (-8)² - 4×1×15 = 64 - 60 = 4 = 2²

D>0, 2 корня

$x_{1}=\frac{-(-8)+2}{2*1} = \frac{8+2}{2} = \frac{10}{2} = 5\\x_{2} = \frac{-(-8)-2}{2*1} = \frac{8-2}{2} = \frac{6}{2} = 3$

Ответ: x₁ = 5 ; x₂ = 3