当0当0当01=x²+1-x²=x²+(1-x²)/2+(1-x²)/2≥3[x²(1-x²)²/4]^(1/3)所以2√3/9≥x(1-x²)即x(1-x²)最大值为2√3/9当且仅当x²=(1-x²)/2,即x=√3/3时等号成立
当01=x²+1-x²=x²+(1-x²)/2+(1-x²)/2≥3[x²(1-x²)²/4]^(1/3)所以2√3/9≥x(1-x²)即x(1-x²)最大值为2√3/9当且仅当x²=(1-x²)/2,即x=√3/3时等号成立