化简求值已知X+Y+Z=0 ,求(1/Y2+Z2-X2)+(1/Z2+X2-Y2)+1/X2+Y2-Z2)的值

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化简求值已知X+Y+Z=0,求(1/Y2+Z2-X2)+(1/Z2+X2-Y2)+1/X2+Y2-Z2)的值化简求值已知X+Y+Z=0,求(1/Y2+Z2-X2)+(1/Z2+X2-Y2)+1/X2+

化简求值已知X+Y+Z=0 ,求(1/Y2+Z2-X2)+(1/Z2+X2-Y2)+1/X2+Y2-Z2)的值
化简求值
已知X+Y+Z=0 ,求(1/Y2+Z2-X2)+(1/Z2+X2-Y2)+1/X2+Y2-Z2)的值

化简求值已知X+Y+Z=0 ,求(1/Y2+Z2-X2)+(1/Z2+X2-Y2)+1/X2+Y2-Z2)的值
x+z=-y
x+y=-z
所以y²+z²-x²
=y²+(x+z)(z-x)
=y²-y(z-x)
=y(y-z+x)
=y(-z-z)
=-2yz
同理
z²+x²-y²=-2zx
x²+y²-z²=-2xy
原式=-1/2*(1/xy+1/yz+1/xz)
=-1/2*(x+y+z)/xyz
=0