已知x,y∈R,满足（x²+y²+2)(x²+y²-1)-18≤0.求证：xy≤2

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已知x,y∈R,满足（x²+y²+2)(x²+y²-1)-18≤0.求证：xy≤2
已知x,y∈R,满足（x²+y²+2)(x²+y²-1)-18≤0.求证：xy≤2

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

（x²+y²+2)(x²+y²-1)≤18等价于（x²+y²)^2+(x²+y²)≤20
2xy*(2xy+1)≤（x²+y²)^2+(x²+y²)≤20
(2xy+1/2)^2-1/4≤20
(2xy+1/2)^2≤81/4
2xy+1/2≤9/2
2xy≤4
xy≤2
清楚吧

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