若(z-x)2-4(x-y)(y-z)=0,求x+z-2y+2009
问题描述：
若(z-x)2-4(x-y)(y-z)=0,求x+z-2y+2009
如题
答
(z-x)²-4(x-y)(y-z)
=(x-z)²-4(x-y)(y-z)
=[(x-y)+(y-z)]²-4(x-y)(y-z)
=(x-y)²+2(x-y)(y-z)+(y-z)²-4(x-y)(y-z)
=(x-y)²-2(x-y)(y-z)+(y-z)²
=[(x-y)-(y-z)]²
=(x+z-2y)²=0
x+z-2y=0
所以x+z-2y+2009=2009