Реши уравнения: a) x²-5(x+1) = -5

a) $x^2 - 5(x+1) = -5$ $x^2 - 5x - 5 = -5$ $x^2 - 5x = 0$ $x(x-5) = 0$ $x_1 = 0$, $x_2 = 5$ б) $2x^4 + 9x^2 + 10 = 15$ $2x^4 + 9x^2 - 5 = 0$ Пусть $y = x^2$, тогда $2y^2 + 9y - 5 = 0$ $D = 81 - 4 * 2 * (-5) = 81 + 40 = 121$ $y_1 = (-9 + 11) / 4 = 0.5$ $y_2 = (-9 - 11) / 4 = -5$ $x^2 = 0.5$ => $x = \pm \sqrt{0.5}$ $x^2 = -5$ - нет решений в) $x^3 - x - 2x^2 + 2 = 0$ $x(x^2 - 1) - 2(x^2 - 1) = 0$ $(x-2)(x^2 - 1) = 0$ $(x-2)(x-1)(x+1) = 0$ $x_1 = 2$, $x_2 = 1$, $x_3 = -1$ г) $\frac{x^2 - 6x}{x-1} + \frac{5}{x-1} = 0$ ОДЗ: $x \neq 1$ $\frac{x^2 - 6x + 5}{x-1} = 0$ $x^2 - 6x + 5 = 0$ $D = 36 - 4 * 5 = 16$ $x_1 = (6 + 4) / 2 = 5$ $x_2 = (6 - 4) / 2 = 1$ (не подходит из-за ОДЗ) д) $(x^2 - 5x + 4)(x^2 - 5x + 1) = 28$ Пусть $y = x^2 - 5x$, тогда $(y + 4)(y + 1) = 28$ $y^2 + 5y + 4 = 28$ $y^2 + 5y - 24 = 0$ $D = 25 - 4 * (-24) = 25 + 96 = 121$ $y_1 = (-5 + 11) / 2 = 3$ $y_2 = (-5 - 11) / 2 = -8$ $x^2 - 5x = 3$ => $x^2 - 5x - 3 = 0$ $D = 25 - 4 * (-3) = 37$ $x_1 = (5 + \sqrt{37}) / 2$ $x_2 = (5 - \sqrt{37}) / 2$ $x^2 - 5x = -8$ => $x^2 - 5x + 8 = 0$ $D = 25 - 4 * 8 = -7$ - нет решений