(Z-X)"-4(X-Y)(Y-Z)=0 证明X-2Y+Z=0 ‘"’是平方

来源：学生作业帮助网编辑：作业帮时间：2024/05/01 17:17:08

(Z-X)"-4(X-Y)(Y-Z)=0 证明X-2Y+Z=0 ‘"’是平方
(Z-X)"-4(X-Y)(Y-Z)=0 证明X-2Y+Z=0 ‘"’是平方

(Z-X)"-4(X-Y)(Y-Z)=0 证明X-2Y+Z=0 ‘"’是平方
因为：(z-x)^2-4(x-y)(y-z)=0
所以：[(x-y)+(y-z)]^2-4(x-y)(y-z)=0
所以：(x-y)^2+2(x-y)(y-z)+(y-z)^2-4(x-y)(y-z)=0
即：(x-y)^2-2(x-4)(y-z)+(y-z)^2=0
所以：[(x-y)-(y-z)]^2=0
所以：x-2y+z=0

x-y=a，y-z=b，则x-z=a+b
(z-x)^2-4(x-y)(y-z)=0
(a+b)^2-4ab=0
(a-b)^2=0
a=b
x-2y+z=(x-y)+(z-y)=a-b=0

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