Ты просишь меня решить уравнения: y³ – 6y = 0; 6x⁴ + 3,6x² = 0; x³ + 3x = 3,5x²; x³ – 0,1x = 0,3x²; 9х³ – 18x² − x + 2 = 0; у⁴ - у³ – 16y² + 16y = 0; р³ - р² = р – 1; x⁴ - x² = 3x³ – 3x.

a) $y^3 - 6y = 0$ $y(y^2 - 6) = 0$ $y_1 = 0$ $y^2 - 6 = 0$ $y^2 = 6$ $y_2 = \sqrt{6}$ $y_3 = -\sqrt{6}$ б) $6x^4 + 3.6x^2 = 0$ $x^2(6x^2 + 3.6) = 0$ $x_1 = 0$ $6x^2 + 3.6 = 0$ $6x^2 = -3.6$ $x^2 = -0.6$ (нет решений, так как квадрат не может быть отрицательным) в) $x^3 + 3x = 3.5x^2$ $x^3 - 3.5x^2 + 3x = 0$ $x(x^2 - 3.5x + 3) = 0$ $x_1 = 0$ $x^2 - 3.5x + 3 = 0$ $D = (-3.5)^2 - 4 * 1 * 3 = 12.25 - 12 = 0.25$ $x_2 = (3.5 + \sqrt{0.25}) / 2 = (3.5 + 0.5) / 2 = 4 / 2 = 2$ $x_3 = (3.5 - \sqrt{0.25}) / 2 = (3.5 - 0.5) / 2 = 3 / 2 = 1.5$ г) $x^3 - 0.1x = 0.3x^2$ $x^3 - 0.3x^2 - 0.1x = 0$ $x(x^2 - 0.3x - 0.1) = 0$ $x_1 = 0$ $x^2 - 0.3x - 0.1 = 0$ $D = (-0.3)^2 - 4 * 1 * (-0.1) = 0.09 + 0.4 = 0.49$ $x_2 = (0.3 + \sqrt{0.49}) / 2 = (0.3 + 0.7) / 2 = 1 / 2 = 0.5$ $x_3 = (0.3 - \sqrt{0.49}) / 2 = (0.3 - 0.7) / 2 = -0.4 / 2 = -0.2$ д) $9x^3 - 18x^2 - x + 2 = 0$ $9x^2(x - 2) - 1(x - 2) = 0$ $(9x^2 - 1)(x - 2) = 0$ $x - 2 = 0$ $x_1 = 2$ $9x^2 - 1 = 0$ $9x^2 = 1$ $x^2 = 1/9$ $x_2 = 1/3$ $x_3 = -1/3$ е) $y^4 - y^3 - 16y^2 + 16y = 0$ $y(y^3 - y^2 - 16y + 16) = 0$ $y_1 = 0$ $y^3 - y^2 - 16y + 16 = 0$ $y^2(y - 1) - 16(y - 1) = 0$ $(y^2 - 16)(y - 1) = 0$ $y - 1 = 0$ $y_2 = 1$ $y^2 - 16 = 0$ $y^2 = 16$ $y_3 = 4$ $y_4 = -4$ ж) $p^3 - p^2 = p - 1$ $p^3 - p^2 - p + 1 = 0$ $p^2(p - 1) - 1(p - 1) = 0$ $(p^2 - 1)(p - 1) = 0$ $p - 1 = 0$ $p_1 = 1$ $p^2 - 1 = 0$ $p^2 = 1$ $p_2 = 1$ $p_3 = -1$ з) $x^4 - x^2 = 3x^3 - 3x$ $x^4 - 3x^3 - x^2 + 3x = 0$ $x(x^3 - 3x^2 - x + 3) = 0$ $x_1 = 0$ $x^3 - 3x^2 - x + 3 = 0$ $x^2(x - 3) - 1(x - 3) = 0$ $(x^2 - 1)(x - 3) = 0$ $x - 3 = 0$ $x_2 = 3$ $x^2 - 1 = 0$ $x^2 = 1$ $x_3 = 1$ $x_4 = -1$ *Перевод:* а) y³ – 6y = 0; б) 6x4 + 3,6x2 = 0; в) x³ + 3x = 3,5x²; г) x³ – 0,1x = 0,3x²; д) 9х³ – 18x2 − x + 2 = 0; е) у4 - у³ – 16y² + 16y = 0; ж) р³ - р² = р – 1; з) x⁴ - x² = 3x³ – 3x.