Question

已知x-y=6,z-y=10,则代数式x平方+y平方+z平方-xy-yz-xz的值为?

Answer 1

x-y=6,z-y=10

x-z=(x-y)-(z-y)=6-10=-4

x平方+y平方+z平方-xy-yz-xz

=(2x^2+2y^2+2z^2-2xy-2yz-2xz)/2

=((x^2-2xy+y^2)+(y^2-2yz+z^2)+(z^2-2xz+x^2))/2

=((x-y)^2+(y-z)^2+(z-x)^2)/2

=(6^2+10^2+(-4)^2)/2

=(36+100+16)/2

=152/2

=76