Решите уравнение 1/x² – 1/x – 6 = 0.

Источник: Ященко ОГЭ 2025 (36 вар.)

Решение:

1/x² – 1/x – 6 = 0

1/x² – 1/x – 6 = 0

1 – x – 6x² = 0

-6x² + x – 1 = 0

D = 1² ⋅ 4 ⋅ 6 ⋅ (-1) = 25 = 5²

x₁ = – 1 + 5 / 2 ⋅ 6 = 4 / 12 = 1/3

x₂ = – 1 – 5 / 2 ⋅ 6 = -6 / 12 = – 0,5

Ответ: -0,5; 1/3