Question

若（z-x）²-4(x-y)(y-z)=0,求证2y=x+z

Answer 1

若（z-x）²-4(x-y)(y-z)=0,求证2y=x+z

(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2y=x+z