Question

Решить уравнение ...........

Answer 1

Ответ:

$x_1 = \frac{5}{6} \\ x_2 = 1.5$

Пошаговое объяснение:

$\frac{1}{ {(x - 1)}^{2} } + \frac{4}{x - 1} - 12 = 0 \: \: \: \: \: \: \: | \: x≠ 1 \\ \frac{1 + 4(x - 1) - 12 {(x - 1)}^{2}}{ {(x - 1)}^{2} } = 0 \\ 1 + 4x - 4 - 12( {x}^{2} - 2x + 1) = 0 \\ 1 + 4x - 4 - 12 {x}^{2} + 24x - 12 = 0 \\ - 12 {x}^{2} + 28x - 15 = 0 \\ D = {28}^{2} - 4 \times ( - 12) \times ( - 15) = 784 - 720 = 64 \\ \sqrt{D} = \sqrt{64} = 8 \\ x_1 = \frac{ - 28 + 8}{2 \times ( - 12)} = \frac{ - 20}{ - 24} = \frac{5}{6} \\ x_2 = \frac{ - 28 - 8}{2 \times ( - 12)} = \frac{ - 36}{ - 24} = \frac{3}{2} = 1.5$