因为x-y=a,z-y=10
所以x-z=a-10
x×x＋y×y＋z×z－xy－yz－zx
=x²+y²+z²-xy-yz-zx
=1/2(2x²+2y²+2z²-2xy-2yz-2zx)
=1/2[(x²-2xy-y²)+(x²-2xz-z²)+(z²-2yz-y²)]
=1/2[(x-y)²+(x-z)²+(y-z)²]
=1/2[a²+(a-10)²+10²]
=1/2(a²+100+a²-20a+100)
=1/2(2a²-20a+200)
=a²-10a+100