Question

Решите пожалуйста уравнение: (x-4)(x-5)(x-6)=(x-2)(x-5)(x-6)

Answer 1

$(x - 4)(x - 5)(x - 6) = (x - 2)(x - 5)(x - 6) \\ \\ (x - 4)(x - 5)(x - 6) - (x - 2)(x - 5)(x - 6) = 0 \\ \\ (x - 5)(x - 6) \times ( \: (x - 4) - (x - 2) \: ) = 0 \\ \\ (x - 5)(x - 6)(x - 4 - x + 2) = 0 \\ \\ (x - 5)(x - 6) \times ( - 2) = 0 \\ \\ 1) \: \: x - 5 = 0 \\ \: \: \: \: \: \: x = 5 \\ \\ 2) \: \: x - 6 = 0 \\ \: \: \: \: \: \: x = 6$

Ответ: 5 ; 6