已知实数xyz满足式子（x-z）的平方-4(x-y)(y-z)=0,问怎么推出x+z=2y诺不能,还能推出什么公式?

Question

已知实数xyz满足式子（x-z）的平方-4(x-y)(y-z)=0 ,问怎么推出x+z=2y诺不能,还能推出什么公式?

Answer 1

(x-z)²-4(x-y)(y-z)=0
[(x-y)+(y-z)]²-4(x-y)(y-z)=0
(x-y)²+2(x-y)(y-z)+(y-z)²-4(x-y)(y-z)=0
(x-y)²-2(x-y)(y-z)+(y-z)²=0
[(x-y)-(y-z)]²=0
(x-y)-(y-z)=0
即x+z=2y