Реши уравнение: 2x(x−19)²−x²(x−19)=0 (три корня)

Здравствуйте!

Вот ваше решение:

$2x(x-19)^{2}- x^{2}(x-19) = 0\\2x(x^{2} -38+361) - x^{3}+19x^{2} = 0\\2x^{3} -76x^{2} +722x - x^{3} +19x^{2} \\x^{3} - 76x^{2} +722x+19x^{2} = 0\\x^{3}-57x^{2}+722x = 0\\x(x^{2}-75x+722)=0\\x(x^{2}-19x-38x+722)=0\\x(x(x-19)-38(x-19)) = 0\\x(x-19)(x-38) = 0\\x = 0\\x - 19 = 0\\x - 38 = 0\\\\x_{1} = 0\\x_{2} = 19\\x_{3} = 38$