Question

Алгебра. Решить примеры:
1) $x^{2}$ = -9x - 8
2) $x^{2}$ - 20x = -5x - 13 - $x^{2}$

Answer 1

1) x² = -9x - 8; x² + 9x + 8 = 0; x₁ = 8; x₂ = 1. Ответ: 8; 1.

2) x² - 20x = -5x - 13 - x²; x² + x² + 5x - 20x + 13 = 0;  2x² - 15x + 13 = 0;

D = b² - 4ac = 225 - 4·2·13 = 225 - 104 = 121; √D = 11;

x₁ = (15 + 11)/4 = 6,5; x₂ = (15 - 11)/4 = 1.

Ответ: 6,5; 1.

Answer 2

x² = -9x - 8

x² + 9x + 8 = 0

x² +8x + x + 8 =0

x(x+8)+x + 8 = 0

(x +8)(x+1) = 0

x+8=0
x+1=0

x=-8
x=-1

x1=-8
x2=-1


2)
x² - 20x = -5x - 13 - x²

x² - 20x + 5x + 13 + x² = 0

2x² - 15x + 13 = 0

2x² - 2x - 13x + 13 = 0

2x(x-1) - 13(x -1) = 0

(x-1)(2x -13) = 0

x-1 = 0
2x - 13 = 0

x= 1
x = 13/2 = 6,5

x1= 1
x2 = 6,5