x2+y2+z2=xy+yz+zx求〔x-zy+z〕的2010次方的值

题目

x2+y2+z2=xy+yz+zx求〔x-zy+z〕的2010次方的值

答案

x²+y²+z²=xy+yz+zxx²+y²+z²-xy-yz-xz=0两边乘22x²+2y²+2z²-2xy-2yz-2xz=0(x²-2xy+y²)+(y²-2yz+z²)+(z²-2xz+x²)=0(x-y)²+(y-z)&su...