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 x2-4y2-3xy+y+x 2(x-xy)-3(2x2-3xy）2[x2（2x2-xy+y2)] (x-y)(x2+xy+y2) (x+y)(x2-xy+y2) 计算(x+y/x-y + 4xy/y2-x2)(x2-9y2)/（x2+2xy-3y2）已知实数x,y满足x2+xy+y2=3,则x2-xy+y2的最小值因式分解x2+xy-3y2 X2+3xy+y2因式分解已知：实数 x y z 不全为 0 求证：√x2+xy+y2 + √y2+yz+z2 + √z2+zx+x2 >3/2 (x+y+z) (x2+xy+y2)-4xy(x2+y2) 解方程组①x2-y2=3x+3y②x2-xy+y2=27 如果2/x=3/y,那么x2-2xy+3y2/7x2-y2? 4x2-3y2+2xy-4x2+5x2 若X2+xy-2y2=0,则（x2+3xy+y2)/x2+y2=? x,y,z为正实数求证 x2/(y2+z2+yz)+y2/(z2+x2+zx)+z2/(x2+y2+xy)>=1 4x2-y2/x2-2xy+y2 +(2x-y)/2x2-2xy 2(x2-xy)-3(2x2-3xy)-2[x2-(2x2-xy+y2)] 化简.