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由(x^2+y^2+z^2)*(x+y+z)=x^3+y^3+z^3+(x+y)z^2+(y+z)x^2+(x+z)y^2,得到(x+y)z^2+(y+z)x^2+(x+z)y^2求解
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由(x^2+y^2+z^2)*(x+y+z)=x^3+y^3+z^3+(x+y)z^2+(y+z)x^2+(x+z)y^2,得到(x+y)z^2+(y+z)x^2+(x+z)y^2求解
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答案和解析
xy+yz+xz={(x²+y²+z²+2xy+2xz+2yz)-(x²+y²+z²)}\2={(x+y+z)²-(x²+y²+z²)}\2=-1\2
(x+y+z)³=x³+y³+z³+2x²(y+z)+2y²(x+z)+2z²(x+y)
(x+y+z)(x²+y²+z²)= x³+y³+z³+x²(y+z)+y²(x+z)+z²(x+y)
x²(y+z)+y²(x+z)+z²(x+y)=(x+y+z)³-(x+y+z)(x²+y²+z²)=1-2=-1
x³+y³+z³=(x+y+z)(x²+y²+z²)- {x²(y+z)+y²(x+z)+z²(x+y)}=3
希望对你能有所帮助.
(x+y+z)³=x³+y³+z³+2x²(y+z)+2y²(x+z)+2z²(x+y)
(x+y+z)(x²+y²+z²)= x³+y³+z³+x²(y+z)+y²(x+z)+z²(x+y)
x²(y+z)+y²(x+z)+z²(x+y)=(x+y+z)³-(x+y+z)(x²+y²+z²)=1-2=-1
x³+y³+z³=(x+y+z)(x²+y²+z²)- {x²(y+z)+y²(x+z)+z²(x+y)}=3
希望对你能有所帮助.
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