已知x,y∈R,满足（x²+y²+2)(x²+y²-1)-18≤0.求证：xy≤2
问题描述：
已知x,y∈R,满足（x²+y²+2)(x²+y²-1)-18≤0.求证：xy≤2
答
（x²+y²+2)(x²+y²-1)≤18等价于（x²+y²)^2+(x²+y²)≤202xy*(2xy+1)≤（x²+y²)^2+(x²+y²)≤20(2xy+1/2)^2-1/4≤20(2xy+1/2)^2≤81/42xy+1/2≤9/22xy≤4...