先求x^2(1-x^2)的最大值
x^2(1-x^2)≤{[x^2+(1-x^2)]/2}^2=1/4
当且仅当x^2=1-x^2时成立
所以-1/2≤x√(1-x^2)≤1/2
所以x√(1-x^2)最大值=1/2
此时x^2=1-x^2且x>0
所以x=√2/2