16cos^4 (x) + sin^2 (x) =7/4

Найдем корень уравнения.

16 * cos^4 (x) + sin^2 (x) = 7/4;

Умножим на 4.

16 * 4 *  cos^4 (x) + 4 * sin^2 (x) = 7/4 * 4; 

64 * cos^4 x + 4 * sin^2 x = 7;

64 * cos^4 x + 4 * sin^2 x 7 = 0;  

64 * cos^4 x + 4 * (1 cos^2 x) 7 = 0;

64 * cos^4 x + 4 * 1 4 * cos^2 x 7 = 0;

64 * cos^4 x 4 * cos^2 x 3 = 0;

Пусть cos^2 x = a, тогда:

64 * a^2 4 * a 3 = 0;

D = (-4)^2 4 * 64 * (-3) = 16 + 16 * 64 = 16 * 65 = 1 040;

a1 = (4 + 1040)/(2 * 64) = (4 + 4 * 65)/(2 * 64) = (1 + 65)/(2 * 16) = (1 + 65)/32;

a2 = (1 - 65)/32;

1) cos^2 x = (1 + 65)/32;

cos x = +-((1 + 65)/32); 

x = +-arccos (((1 + 65)/32) + 2 * pi * n;

x =   +-arccos (-((1 + 65)/32) + 2 * pi * n;

2) cos^2 x = (1 - 65)/32;

cos x = +-((1 - 65)/32); 

x = +-arccos (((1 - 65)/32) + 2 * pi * n;

x =   +-arccos (-((1 - 65)/32) + 2 * pi * n, n Z.