已知x-y=5,y-z=4,求xx+yy+zz-xy-yz-xz的值

题目

已知x-y=5,y-z=4,求xx+yy+zz-xy-yz-xz的值

答案

x-z=(x-y)+(y-z)=5+4=9(x-y)²=x²-2xy+y²=25(y-z)²=y²-2yz+z²=16(x-z)²=x²-2xz+z²=81上面的三个式子相加得x²-2xy+y²+y²-2yz+z²+x²-2xz+z&sup...