Question

Решить примеры через дискриминант:
1) 2а^2-а=3
2) -t^2+t+3=0

, . 35 .

Answer 1

$1) \: 2 {a}^{2} - a - 3 = 0 \\ d = 1 - 4 \times 2 ( - 3) = 25 \\ x1 = \frac{1 - 5}{2 \times 2} = - 2 \\ x2 = \frac{1 + 5}{2 \times 2} = 1.5 \\ - {t}^{2} + t + 3 = 0 \\ {t}^{2} - t - 3 = 0 \\ d = 1 - 4 \times 1 \times( - 3) = 13 \\ x1 = \frac{1 - \sqrt{13} }{2} \\ x2 = \frac{1 +\sqrt{13} }{2}$

Answer 2

$1)2a {}^{2} - a = 3 \\ 2a {}^{2} - a - 3 = 0 \\ d = ( - 1) {}^{2} - 4 \times 2 \times ( - 3) = 1 + 24 = 25 \\ a _{1} = \frac{1 - 5}{2 \times 2} = \frac{ - 4}{4} = - 1 \\ a _{2} = \frac{1 + 5}{2 \times 2} = \frac{6}{4} = \frac{3}{2} = 1.5$

$- t {}^{2} + t + 3 = 0 \\ t {}^{2} - t - 3 = 0 \\ d = ( - 1) {}^{2} - 4 \times 1 \times ( - 3) = 1 + 12 = 13 \\ t _{1} = \frac{1 - \sqrt{13} }{2} \\ t _{2} = \frac{1 + \sqrt{13} }{2}$