x-y=6,y-z=5,求x的平方+y的平方+z的平方-xy-yz-zx

x的平方+y的平方+z的平方-xy-yz-zx
=x的平方-xy+y的平方-yz+z的平方-zx
=X(X-Y)+Y(Y-Z)+Z(Z-X)
代入X-Y=6(1),Y-Z=5(2),(1)+(2)得X-Z=11,即Z-X=-11(3),
=6X+5Y-11Z
=6X-6Y+6Y+5Y-11Z
=6X-6Y+11Y-11Z
=6(X-Y)+11(Y-Z)
代入X-Y=6(1),Y-Z=5(2),
=6*6+11*5
=36+55
=91

x-y=6
y-z=5
将上述2式子相加得x-z=11
x的平方+y的平方+z的平方-xy-yz-zx
=(（x-y）^2（y-z）^2（x-z）^2)/2
=(6^2*5^2*11^2)/2
=91
谢谢~

由x-y=6,y-z=5可知x-z=11
(x-y)2=x2+y2-2xy=36
(y-z)2=y2+z2-2yz=25
(x-z)2=x2+z2-2xz=121
将上面三个式子相加
得x2+y2-2xy+y2+z2-2yz+x2+z2-2xz=182
在除以2
得x2+y2+z2-xy-yz-zx=91

原式=½(2x²+2y²+2z²-2xy-xyz-2zx)
=½(x²+y²-2xy)+½(x²+z²-2xz)+½(y²+z²-2yz)
=½（x-y）²+½（x-z）²+½（y-z）²
x-z=11