Question

помогите решить уравнение
1.sin 2x=-√2/2;
2. 2cos²x+cos x-6=0

Answer 1

1)
$sin(2x ) = - sqrt{2} div 2 \ 2x = - {1}^{k} times arcsin ( - frac{ sqrt{2} }{2}) + pi times k \ 2x = - {1}^{k} times ( - frac{pi}{4}) + pi times k \ x = - {1}^{k} times ( - frac{pi}{8} ) + frac{pi times k}{2}$
2)
$2 {cos}^{2} x + cos(x ) - 6 = 0 \ cos(x) = t \2 {t}^{2} + t - 6 = 0 \ d = 1 + 24 = 25 \ x1 = frac{ - 1 + 5}{4} = 1 \ x2 = frac{ - 1 - 5}{4} = - frac{6}{4} \ cos(x) = 1 \ x = 2pi : k$