Question

若x-3=y-2=z-1,求x^+y^+z^-xy-yz-xz的值,

Answer 1

x-3=y-2

x-y=1

y-2=z-1

y-z=1

x-3=z-1

z-x=-2

x^2+y^2+z^2-xy-yz-xz

=x(x-y)+y(y-z)+z(z-x)

=x+y-2z

x-3=z-1

y-2=z-1

2式相加,得

x+y-5=2z-2

x+y-2z=3

原式=3