Question

若(z-x)的二次方-4(x-y)(y-z)=0,求证x-2y+z=0

Answer 1

证明:∵(z-x)的二次方-4(x-y)(y-z)
=z的二次方-2zx+x的二次方-4xy-4yz+4xz+4y的二次方
=(x+z-2y)的二次方
∵(x+z-2y)的二次方=0
∴x2y+z=0
答:__________________。

Answer 2

z-x=-(y-z)-(x-y)
记x-y=u,
y-z=v
故原式等价为(u+v)^2-4uv=0
即(u-v)^2=0
故u=v
即x-y=y-z
即x-2y+z=0

Answer 3

(z-x)的二次方-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)^
=[(x-y)-(y-z)]^2=0
故x-y-y+z=0
x-2y+z=0

Answer 4

X-2Y+Z=0;可以变形为X-Y-Y+Z=0，再变形为X-Y+Z-Y=0
z-x=(x-y)+(y-z)
∵(z-x)^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
=[(x-y)-(y-z)]^2=0
∴x-y-y+z=0
∴x-2y+z=0

Answer 5

你的题意不太明白，不过我可以给你提示两个因式相乘得0，则这两个式子必有一个为0或两个都为0.
在变形要证因式：
X-2Y+Z=0;可以变形为X-Y-Y+Z=0，在变形为X-Y+Z-Y=0