假设x=asinb,y=acosb,其中1≤a≤2^0.5
x^-xy+y^
=a^2-a^2sinbcosb
=a^2-1/2a^2sin2b
其中
-1≤sin2b≤1
那么
a^2-1/2a^2=1/2a^2≤a^2-1/2a^2sin2b≤a^2+1/2a^2=3/2a^2
则
1/2a^2≤x^-xy+y^≤3/2a^2
1/2*1≤x^-xy+y^≤3/2*2
则1/2≤x^-xy+y^≤3
证毕
假设x=asinb,y=acosb,其中1≤a≤2^0.5
x^-xy+y^
=a^2-a^2sinbcosb
=a^2-1/2a^2sin2b
其中
-1≤sin2b≤1
那么
a^2-1/2a^2=1/2a^2≤a^2-1/2a^2sin2b≤a^2+1/2a^2=3/2a^2
则
1/2a^2≤x^-xy+y^≤3/2a^2
1/2*1≤x^-xy+y^≤3/2*2
则1/2≤x^-xy+y^≤3
证毕