已知三个实数x,y,z满足(z-x)平方-4(x-y)(y-z)=0.求证x,y,z成等差数列

已知三个实数x,y,z满足(z-x)平方-4(x-y)(y-z)=0.求证x,y,z成等差数列
已知三个实数x,y,z满足(z-x)平方-4(x-y)(y-z)=0.求证x,y,z成等差数列

已知三个实数x,y,z满足(z-x)平方-4(x-y)(y-z)=0.求证x,y,z成等差数列
(z-x)²-4(x-y)(y-z)=0.
z²+x²-2xz-4（xy-xz-y²+yz）=0
z²+x²+2xz-4xy+4y²-4yz=0
（z+x）²-4（（x+z）y+4y²=0
（x+z-2y）²=0
2y=x+z
所以x,y,z成等差数列