已知x-y=1/2+√3,y-z=1/2-√3,求x²+y²+z²-xy-xz-yz的值

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已知x-y=1/2+√3,y-z=1/2-√3,求x²+y²+z²-xy-xz-yz的值
已知x-y=1/2+√3,y-z=1/2-√3,求x²+y²+z²-xy-xz-yz的值

已知x-y=1/2+√3,y-z=1/2-√3,求x²+y²+z²-xy-xz-yz的值
原式=1/2（2x^2+2y^2=2z^2-2xz-2xy-2yz)
=1/2[(x-y)^2+(x-z)^2+(y-z)^2]
由x-y=1/2+√3,y-z=1/2-√3得x-z=2√3
将x-y=1/2+√3,y-z=1/2-√3,x-z=2√3代入得
原式=31/2

原式=1/2（2x^2+2y^2=2z^2-2xz-2xy-2yz)
=1/2[(x-y)^2+(x-z)^2+(y-z)^2]
下面就请代进自己算吧希望采纳哟

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