1°. Решите уравнение: a) $$2x^2 - 11x + 12 = 0$$ б) $$14x^2 = 9x$$ в) $$16x^2 - 49 = 0$$ г) $$x^2 - 36x + 323 = 0$$.

Решение: a) $$2x^2 - 11x + 12 = 0$$ Дискриминант: $$D = (-11)^2 - 4 * 2 * 12 = 121 - 96 = 25$$ $$x_1 = (11 + \sqrt{25}) / (2 * 2) = (11 + 5) / 4 = 16 / 4 = 4$$ $$x_2 = (11 - \sqrt{25}) / (2 * 2) = (11 - 5) / 4 = 6 / 4 = 1.5$$ Ответ: $$x_1 = 4$$, $$x_2 = 1.5$$ б) $$14x^2 = 9x$$ $$14x^2 - 9x = 0$$ $$x(14x - 9) = 0$$ $$x_1 = 0$$ $$14x - 9 = 0$$ $$14x = 9$$ $$x_2 = 9/14$$ Ответ: $$x_1 = 0$$, $$x_2 = 9/14$$ в) $$16x^2 - 49 = 0$$ $$16x^2 = 49$$ $$x^2 = 49/16$$ $$x_1 = \sqrt{49/16} = 7/4 = 1.75$$ $$x_2 = -\sqrt{49/16} = -7/4 = -1.75$$ Ответ: $$x_1 = 1.75$$, $$x_2 = -1.75$$ г) $$x^2 - 36x + 323 = 0$$ Дискриминант: $$D = (-36)^2 - 4 * 1 * 323 = 1296 - 1292 = 4$$ $$x_1 = (36 + \sqrt{4}) / (2 * 1) = (36 + 2) / 2 = 38 / 2 = 19$$ $$x_2 = (36 - \sqrt{4}) / (2 * 1) = (36 - 2) / 2 = 34 / 2 = 17$$ Ответ: $$x_1 = 19$$, $$x_2 = 17