(x^2)+(y^2)+(z^2)^-2(x+y+z)+3=0 求x^3+y^3+z^3+3xyz=
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![(x^2)+(y^2)+(z^2)^-2(x+y+z)+3=0 求x^3+y^3+z^3+3xyz=](/uploads/image/z/9315779-59-9.jpg?t=%28x%5E2%29%2B%28y%5E2%29%2B%28z%5E2%29%5E-2%28x%2By%2Bz%29%2B3%3D0+%E6%B1%82x%5E3%2By%5E3%2Bz%5E3%2B3xyz%3D)
(x^2)+(y^2)+(z^2)^-2(x+y+z)+3=0 求x^3+y^3+z^3+3xyz=
(x^2)+(y^2)+(z^2)^-2(x+y+z)+3=0 求x^3+y^3+z^3+3xyz=
(x^2)+(y^2)+(z^2)^-2(x+y+z)+3=0 求x^3+y^3+z^3+3xyz=
(x^2)+(y^2)+(z^2)-2(x+y+z)+3=0 求x^3+y^3+z^3+3xyz=
(x^2)+(y^2)+(z^2)-2(x+y+z)+3=0
(x^2-2x+1)+(y^2-2y+1)+(z^2-2z+1)=0
(x-1)^2+(y-1)^2+(z-1)^2=0
(x-1)^2=0 (y-1)^2=0 (z-1)^2=0
x=1 y=1 z=1
x^3+y^3+z^3+3xyz
=1+1+1+3=6
x^2+y^2+z^2-2(x+y+z)+3=0
x^2+y^2+z^2-2x-2y-2z+3=0
x^2-2x+1+y^2-2y+1+z^2-2z+1=0
(x-1)^2+(y-1)^2+(z-1)^2=0
(x-1)^2=0,(y-1)^2=0,(z-1)^2=0
解得
x=1
y=1
z=1
x^3+y^3+z...
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x^2+y^2+z^2-2(x+y+z)+3=0
x^2+y^2+z^2-2x-2y-2z+3=0
x^2-2x+1+y^2-2y+1+z^2-2z+1=0
(x-1)^2+(y-1)^2+(z-1)^2=0
(x-1)^2=0,(y-1)^2=0,(z-1)^2=0
解得
x=1
y=1
z=1
x^3+y^3+z^3+3xyz
=1^3+1^3+1^3+3*1*1*1
=1+1+1+3
=6
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