设x^2+y^2=1,则x-根号3倍的y的取值范围是

x=cosa y=sina

x-√3y
=cosa-√3sina

-2<=cosa-√3sina<=2

t=x-根号3倍的y
x=t+√3y
(t+√3y)^2+y^2=1
4y^2+2√3ty+t^2-1=0
△=12t^2-4*4(t^2-1)=-4t^2+16≥0
4t^2≤16
-2≤t≤2
即：
x-根号3倍的y的取值范围是：[-2,2]