Как решить уравнение (5x-1)²(x-1)=(5x-1)(x-1)² ?
(5x-1)²(x-1) = (5x-1)(x-1)²
(5x-1)²(x-1) - (5x-1)(x-1)² = 0
(5x-1)(x-1)(5x-1-(x-1)) = 0
(5x-1)(x-1)(5x-1-x+1) = 0
(5x-1)(x-1)(4x) = 0
5x - 1 = 0 или х - 1 = 0 или 4х = 0
5х = 1 х = 1 х = 0
х = 1/5
Ответ: х₁ = 0; х₂ = 1/5; х₃ = 1