已知f(x)=asin2x+cos2x且f(π/3)=√3-1/2
√3-1/2=asin(2π/3)+cos(2π/3)
√3-1/2=a*√3/2-1/2
a=2
y=f(x)=2sin2x+cos2x
y-2sin2x=cos2x=√[1-(sin2x)^2]
y^2+4(sin2x)^2-4y*sin2x=1-(sin2x)^2
5(sin2x)^2-4y*sin2x+y^2-1=0
上方程未知数为(sin2x)的判别式△≥0,即
(4y)^2-4*5*(y^2-1)≥0
y^2≤5
-√5≤y≤√5
答:a=2,f(x)最大值=√5