544. Решите уравнение: a)x²-1/2 -11x = 11; б) x²+x/2 = 8x-7/3 ;

а) $$\frac{x^2 - 1}{2} - 11x = 11$$

$$x^2 - 1 - 22x = 22$$

$$x^2 - 22x - 23 = 0$$

$$D = (-22)^2 - 4 \cdot 1 \cdot (-23) = 484 + 92 = 576$$

$$x_1 = \frac{22 + \sqrt{576}}{2 \cdot 1} = \frac{22 + 24}{2} = \frac{46}{2} = 23$$

$$x_2 = \frac{22 - \sqrt{576}}{2 \cdot 1} = \frac{22 - 24}{2} = \frac{-2}{2} = -1$$

Ответ: $$x_1 = 23$$, $$x_2 = -1$$

б) $$\frac{x^2 + x}{2} = \frac{8x - 7}{3}$$

$$3(x^2 + x) = 2(8x - 7)$$

$$3x^2 + 3x = 16x - 14$$

$$3x^2 - 13x + 14 = 0$$

$$D = (-13)^2 - 4 \cdot 3 \cdot 14 = 169 - 168 = 1$$

$$x_1 = \frac{13 + \sqrt{1}}{2 \cdot 3} = \frac{13 + 1}{6} = \frac{14}{6} = \frac{7}{3}$$

$$x_2 = \frac{13 - \sqrt{1}}{2 \cdot 3} = \frac{13 - 1}{6} = \frac{12}{6} = 2$$

Ответ: $$x_1 = \frac{7}{3}$$, $$x_2 = 2$$