Question

若(z-x)2-4(x-y)(y-z)=0,求x+z-2y+2009

Answer 1

(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