www.bjedu.gov.cn:已知x=1/2 y=1/3 z=1/4 则(xx+yy-zz+2xy)/(xx-yy+zz-2xz) 得多少?

来源：百度文库编辑：中科新闻网时间：2024/04/30 08:07:48

谁会这到题
``帮忙讲解一下
还有这到题:已知a=20002000/20012001,b=20012001/20022002
c=200220002/20032003,比较a,b,c的大小.

x2+y2-z2+2xy/x2-y2+z2-2xz
=(x+y)2-z2/(x-z)2-y2
=(x+y-z)(x+y+z)/(x-y-z)(x-z+y)
=(x+y+z)/(x-y-z)
然后就是代入了

(xx+yy-zz+2xy)/(xx-yy+zz-2xz)
=[(x+y)^2-z^2]/[(x-z)^2-y^2]
=(x+y+z)(x+y-z)/(x-z+y)(x-z-y)
=(x+y+z)/(x-z-y)
=[(6+3+4)/12]/[(6-3-4)/12]
=-13

(X^2+Y^2-Z^2+2XY)(X^2-Y^2+Z^2-2XZ)
=[(X+Y)^2-Z^2]/[(X^2-Z^2)-Y^2]
=(X+Y+Z)(X+Y-Z)/(X-Z+Y)(X-Y-Z)
=(X+Y+Z)(/(X-Y-Z)
=(1/2+1/3+1/4)/(1/2-1/3-1/4)
=-13

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