Question

(2x−1)²=x(2x−1) решить с дискриминантом

Answer 1

$(2x - 1)^2 = x(2x - 1)\\(2x - 1)(2x - 1) = 2x^2 - x\\4x^2 - 2x - 2x + 1 = 2x^2 - x\\4x^2 - 2x - 2x + 1 - 2x^2 + x = 0\\2x^2 -3x + 1 = 0\\D = b^2 - 4ac = (-3)^2 - 4 * 2 * 1 = 9 - 8 = 1\\\sqrt{D} = 1x = \frac{-b ± \sqrt{D} }{2a}\\ x_1 = \frac{3 + 1}{4} = 1\\x_2 = \frac{3 - 1}{4} = 0,5$

Ответ: 1; 0,5.