作业帮求证:(x2-xy+y2)3+(x2+xy+y2)3能被2x2+2y2整除
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求证:(x2-xy+y2)3+(x2+xy+y2)3能被2x2+2y2整除
求证:(x2-xy+y2)3+(x2+xy+y2)3能被2x2+2y2整除
求证:(x2-xy+y2)3+(x2+xy+y2)3能被2x2+2y2整除
(x²-xy+y²)³+(x²+xy+y²)³
立方和
=[(x²-xy+y²)+(x²+xy+y²)][(x²-xy+y²)²-(x²-xy+y²)(x²+xy+y²)+(x²+xy+y²)²]
=(2x²+2y²)[(x²-xy+y²)²-(x²-xy+y²)(x²+xy+y²)+(x²+xy+y²)²]
所以能被2x²+2y²整除
立方和公式
(x²-xy+y²)³+(x²+xy+y²)³
=(x²+xy+y²+x²-xy+y²)[(x²-xy+y²)²-(x²-xy+y²)(x²+xy+y²)+(x²+xy+y²)&su...
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立方和公式
(x²-xy+y²)³+(x²+xy+y²)³
=(x²+xy+y²+x²-xy+y²)[(x²-xy+y²)²-(x²-xy+y²)(x²+xy+y²)+(x²+xy+y²)²]
=(2x²+2y²))[(x²-xy+y²)²-(x²-xy+y²)(x²+xy+y²)+(x²+xy+y²)²]显然能够被(2x²+2y²)整除
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求证:(x2-xy+y2)3+(x2+xy+y2)3能被2x2+2y2整除
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