Решите уравнение (х –1) (х² + 6х + 9) = 5 (х + 3)

Источник : Ященко ОГЭ 2023 (36 вариантов)

Решение:

(х – 1) ∙ (х ² + 6 ∙ х + 9) = 5 ∙ (х + 3)

(x – 1) ∙ (x + 3)² = 5 ∙ (x + 3)

(x – 1) ∙ (x + 3) ² – 5 ∙ (x + 3) = 0

(x + 3) ∙ ((x – 1) ∙ (x + 3) – 5) = 0

1) x + 3 = 0

x = 0 – 3

x = – 3

2) (x – 1) ∙ (x + 3) – 5 = 0

x ² + 3 ∙ x – x – 3 – 5 = 0

x ² + 2 ∙ x – 8 = 0

D = b2 – 4ac = 22 – 4·1·(-8) = 4 + 32 = 36

x₁ = (- 2 – √36) / (2·1) = (-2 – 6) / 2 = -8/2 = – 4

x₂ = (- 2 + √36) / (2·1) = (- 2 + 6) / 2 = 4/2 = 2

Ответ: -4; -3; 2