Решите уравнение x⁴ = (3x − 10)².

Источник: Ященко ОГЭ 2025 (36 вар.)

Решение:

x⁴ = (3x − 10)²

x⁴ – (3x – 10)² = 0

x^2⋅2 – (3x – 10)² = 0

(x²)² – (3x – 10)² = 0

(x² – (3x – 10)) ⋅ (x² + (3x – 10)) = 0

(x² – 3x + 10) ( x² + 3x – 10) = 0

x² – 3x + 10 = 0

D = (-3)² – 4 ⋅ 1 ⋅ 10 = -31 (нет корней)

x² + 3x – 10 = 0

D = 3² – 4 ⋅ 1 (-10) = 49

√49 = 7

x₁ = -3 + 7 / 2 = 4/2 = 2

x₂ = -3 – 7 / 2 = -10/2 = -5

Ответ: -5; 2