Question

若x-y=5,y-z=4,求x的平方+y的平方+z的平方-xy-yz-zx的值.

Answer 1

x²+y²+z²-xy-yz-xz

=(1/2)(2x²+2y²+2z²-2xy-2yz-2zx)

=(1/2)(x²-2xy+y²+y²-2yz+z²+z²-2zx+x²)

=(1/2)[(x-y)²+(y-z)²+(x-z)²]

=(1/2)[(x-y)²+(y-z)²+[(x-y)+(y-z)]²]

=(1/2)[5²+4²+(5+4)²]

=(1/2)(25+16+81)

=61