Question

Найдите корень уравнения
arccos4x+arccos2x=пи/3

Answer 1

arcsin(2x)+arcsin(x)=π/3

cos(arcsin(2x)+arcsin(x))=cos(π/3)
cos(arcsin(2x))*cos(arcsin(x))-sin(arcsin(2x))*sin(arcsin(x))=cos(π/3)
cos(arcsin(2x))*cos(arcsin(x))-2x*x=1/2
корень(1-4х^2)*корень(1-х^2)=1/2+2x^2
2корень(1-4х^2)*корень(1-х^2)=1+4x^2
4*(1-4х^2)*(1-х^2)=(1+4x^2)^2
х^2=t
4*(1-4t)*(1-t)=(1+4t)^2
4*(1-5t+4t^2)=1+8t+16t^2
4-20t=1+8t
3=28t
t=3/28
x=корень(3/28)