实数x,y满足|x+y|≤1,|x-y|≤1.证明|x|+|y|≤1.

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实数x,y满足|x+y|≤1,|x-y|≤1.证明|x|+|y|≤1.
实数x,y满足|x+y|≤1,|x-y|≤1.证明|x|+|y|≤1.

实数x,y满足|x+y|≤1,|x-y|≤1.证明|x|+|y|≤1.
|x+y|≤1 => (x+y)^2≤1 => x^2+2xy+y^2≤1
|x-y|≤1 => (x-y)^2≤1 => x^2-2xy+y^2≤1
x^2+y^2≤1
|x|+|y|≤x^2+y^2≤1

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