哪位帅哥美女能帮忙解这道代数式化简求值的练习题?已知x-y=a,z-y=10,求代数式x×x+y×y+z×z-xy-yz-zx

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哪位帅哥美女能帮忙解这道代数式化简求值的练习题?已知x-y=a,z-y=10,求代数式x×x+y×y+z×z-xy-yz-zx哪位帅哥美女能帮忙解这道代数式化简求值的练习题?已知x-y=a,z-y=1

哪位帅哥美女能帮忙解这道代数式化简求值的练习题?已知x-y=a,z-y=10,求代数式x×x+y×y+z×z-xy-yz-zx
哪位帅哥美女能帮忙解这道代数式化简求值的练习题?
已知x-y=a,z-y=10,求代数式x×x+y×y+z×z-xy-yz-zx

哪位帅哥美女能帮忙解这道代数式化简求值的练习题?已知x-y=a,z-y=10,求代数式x×x+y×y+z×z-xy-yz-zx
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

=2(xx+yy+zz-xy-yz-zx)/2
=[(x-y)(x-y)+(z-y)(z-y)+(x-z)(x-z)]/2
=aa+100+(a-10)(a-10)
=

x-y=a——(1) z-y=10——(2)
→x-z=a-10——(3)
(1)×(2)﹢(2)×(3)﹢(1)×(3)=x×x+y×y+z×z-xy-yz-zx
=a2-10a+100