解方程：4（sin^6 x+cos^6 x)=1,x∈[0.pi/2]

sin^6 x+cos^6 x=1/4
(sin^2 x)^3+(cos^2 x)^3=1/4
(sin^2 x +cos^2 x)(sin^4 x -sin^2 x*cos^2 x+cos^4 x)=1/4
(sin^2 x-cos^2 x)^2+sin^2 x*cos^2 x=1/4
cos^2 2x +(sin^2 2x)/4=1/4
1/4+3/4*cos^2 2x=1/4
所以 cos2x=0
又2x∈[0,pi]
所以,2x=pi/2
=> x=pi/4