Решение №6410 Решите уравнение (5x + 12)(x^2 – 1) = 3x^2 + 3x.

Решение:

(5x + 12)(x² – 1) = 3x² + 3x
(5x + 12)(x – 1)(x + 1) = 3x(x + 1)
(5x + 12)(x – 1)(x + 1) – 3x(x + 1) = 0
(x + 1)((5x + 12)(x – 1) – 3x) = 0
(x + 1)(5x² – 5x + 12x – 12 – 3x) = 0
(x + 1)·(5x² + 4x – 12) = 0

x + 1 = 0
x₁ = –1
или
5x² + 4x – 12 = 0
D = 4² – 4·5·(–12) = 256 = 16²
x_{2}=\frac{-4+16}{2\cdot 5}=\frac{12}{10}=1,2\\x_{3}=\frac{-4-16}{2\cdot 5}=\frac{-20}{10}=-2

Ответ: –2; –1; 1,2.