Question

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

Answer 1

Здравствуйте!

Вот ваше решение:

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