若x-y=m,y-z=n,则x^2+y^2+z^2-xy-yz-zx的值为___

2025-05-14 16:08:24
推荐回答(3个)
回答1:

原式=1/2[(x-y)2+(x-z)2+(y-z)2]
又x-y=m,y-z=n,所以,x-z=m+n, 代入原式。即得m2+n2+mn

回答2:

x^2+y^2+z^2-xy-yz-zx=x(x-y)+y(y-z)+z(z-x)=mx+ny-z(m+n)=m(x-z)+n(y-z)=m(m+n)+n*n

回答3:

x-z=x-y+y-z=m+n