6. Решите уравнение: х(5 – х) – (х – 5) = 0,

х(5 – х) – (х – 5) = 0

5x - x² - x + 5 = 0

-x² + 4x + 5 = 0

x² - 4x - 5 = 0

D = (-4)² - 4(1)(-5) = 16 + 20 = 36

x₁ = (4 + √36) / 2 = (4 + 6) / 2 = 10 / 2 = 5

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

Ответ: x₁ = 5; x₂ = -1