作业帮哪位帅哥美女能帮忙解这道代数式化简求值的练习题?
来源：学生作业帮 编辑：作业帮 分类：综合作业 时间：2024/08/31 01:21:57
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
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
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