若实数X,Y满足X平方+Y平方=1,则(1-XY)(1+XY)的最大值和最小值
人气:417 ℃ 时间:2019-08-20 02:32:15
解答
x^2+y^2=1
-1<=x<=1 -1<=y<=1
x^2+y^2>=2xy
1>=2xy
(xy)^2<=1/4
(1-xy)(1+xy)=1-(xy)^2>=1-1/4=3/4
又因为(xy)^2>=0 所以1-(xy)^2<=1
综合最大值是1,最小值是3/4
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