Question

若x-3=y-2=z-1,求x的平方+y的平方++z的平方-xy-yz-zx的值

Answer 1

x-3=y-2 x-y=1

y-2=z-1 y-z=1

x-z=2

x²+y²+z²-xy-yz-zx

=(1/2)(x²-2xy+y²+y²-2yz+z²+z²-2zx+x²)

=(1/2)[(x-y)²+(y-z)²+(x-z)²]

=(1/2)(1²+1²+2²)

=3