Решите уравнение 2cos^2 x/3 + 3 cos x/3 -2=0 - вопрос №223332022232228656 от Anonim1678 05.04.2023 14:47

Question

Алгебра: Решите уравнение 2cos^2 x/3 + 3 cos x/3 -2=0 2cos^2 x/2 + корень из 3 cos x/2=0

Anonim1678 · Answer

1) 2*cos^2(x/3) + 3*cos(x/3) - 2 = 0Замена: cos(x/3) = t, -1 ≤ t ≤ 12t^2 + 3t - 2 = 0D = 9 + 4*2*2 = 9 + 16 = 25t1 = (-3 + 5)/4 = 2/4 = 1/2t2 = (-3 - 5)/4 = -8/4 = -2 -1 - посторонний кореньcos(x/3) = 1/2(x/3) = +-π/3 + 2πkx = +- π + 6πk2) Замена: cos(x/2) = t, -1≤ t ≤ 12t^2 + √3*t = 0, t*(2t + √3) = 0t1 = 0t2 = -√3/2cos(x/2) = 0, (x/2) = 2πk, x = 4πkcos(x/2) = -√3/2, x/2 = +-5π/6 + 2πk, x = +-5π/3 + 4πk...