Question

помогите!срочно!
найдите все общие корни уравнений
5cos2x+2cosx-3=0 и sin2x+14cos^2x-8=0

Answer 1

$1) \ 5 cos(2x) + 2 cos(x) - 3 = 0 \ 5(2 cos {}^{2} (x) - 1) + 2 cos(x) - 3 = 0 \ 10 { cos {}^{2} ( x) } - 5 + 2 cos(x) - 3 = 0 \ 10 cos {}^{2} (x) + 2 cos(x) - 8 = 0 \ 5 cos {}^{2} (x) + cos(x ) - 4 = 0 \ d = 1 + 4 times 4 times 5 = 81 = {9}^{2} \ cos(x) = frac{ -1 ±9}{10} = - 1 ;frac{4}{5} \ x = pi + 2pi : k : \ x = ±arccos( frac{4}{5} ) + 2pi : k$
$sin(2x) + 14 cos {}^{2} (x) - 8 = 0 \ 14 cos {}^{2} (x) + 2 sin(x) cos(x) - 8 cos {}^{2} (x) - sin {}^{2} (x) = 0 \ 6 cos {}^{2} (x) + 2 sin(x) cos(x) - 8 sin {}^{2} (x) = 0 : : / div cos {}^{2} (x) \ 6 + 2 tan(x) - 8 tan {}^{2} (x) = 0 \ 8 tan {}^{2} (x) - 2 tan(x) - 6 = 0/ div 2 \ 4 tan {}^{2} (x) - tan(x) - 3 = 0 \ d = 1 + 4 times 3 times 4 = 49 = {7}^{2} \ tan(x) = frac{1±7}{8} = 1; - frac{3}{4} \ x = frac{pi}{4} + pi : k \ x = - arctg( frac{3}{4} ) + pi : k$