Решите уравнение х(х² + 4x + 4) = 3(x + 2).

Источник: Ященко ОГЭ 2025 (36 вар.)

Решение:

х ⋅ (х² + 4x + 4) = 3 ⋅ (x + 2)

x ⋅ (x² + 2 ⋅ 2 ⋅ x + 2² ) = 3 ⋅ (x + 2)

x ⋅ (x + 2)² = 3 ⋅ (x + 2)

x ⋅ (x + 2)² – 3 ⋅(x + 2) = 0

(x + 2) ⋅ (x ⋅ (x + 2) – 3) = 0

(x + 2) ⋅ (x² + 2x – 3) = 0

x + 2 = 0

x¹ = -2

x² + 2x – 3 = 0

D = 2² – 4 ⋅ 1 ⋅ (-3) = 4 + 12 = 16 = 4²

x₂ = -2 + 4 / 2 = 2/2 = 1

x₃ = -2 – 4 / 2 = -6/2 = -3

Ответ: -3, -2, 1