Question

4sin^4(2x)+3cos(4x)-1=0 Помогите.....

Answer 1

Так как cos 4x = 1 - 2 sin^2 2x ;
 4 sin^4 2x + 3(1 - 2 sin^2 2x) - 1 = 0;
4 sin^4 2x + 3 - 6 sin^ 2x  - 1 = 0;
4 sin^4 2x - 6 sin^2 2x + 2 = 0;
2 sin^4 2x - 3 sin^2 2x + 1 = 0;
sin^2 2x = t;      - 1 ≤  t  ≤ 1;
2 t^2 - 3 t + 1 = 0;
t1 = 1; ⇒ sin^2 2x = 1;  ⇒ sin 2x = + - 1;⇒ 2x = pi/2 + pi*k;⇒    x = pi + 2 pi*k.
t2 = 1/2;   ⇒ sin^2 2x = 1/2; ⇒sin 2x = + - sgrt2/2; 2x = pi/4 + pik/2; ⇒x = pi/2 + pik; k-Z .
б) x = pi; 3 pi/2.