已知x+y+z=0,求(x+y)(y+z)(z+x)+xyz的值
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已知x+y+z=0,求(x+y)(y+z)(z+x)+xyz的值
已知x+y+z=0,求(x+y)(y+z)(z+x)+xyz的值
已知x+y+z=0,求(x+y)(y+z)(z+x)+xyz的值
x+y+z=0
=>x+y=-z
=>y+z=-x
=>z+x=-y
所以(x+y)(y+z)(z+x)+xyz=-xyz+xyz=0
x+y=-z,y+z=-x,z+x=-y
(x+y)(y+z)(z+x)+xyz=-xyz+xyz=0
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