△=b^2(c-a)^2-4ac(a-b)(b-c)=0
b^2(c-a)^2=4ac(a-b)(b-c)
(c-a)^2/4ac=(a-b)(b-c)/b^2
(c/a-1)(1-a/c)=4(a/b-1)(1-c/b)
ac(1/a-1/c)(1/a-1/c)=4ac(1/b-1/a)(1/c-1/b)
(1/a-1/c)^2=4(1/b-1/a)(1/c-1/b)
设x=1/a,y=1/b,z=1/c
(x-z)^2-4(y-x)(z-y)=0
x^2+z^2-2xz-4yz+4xz+4y^2-4xy=0
(x+z-2y)^2=0
x+z-2y=0
x+z=2y
1/a+1/c=2/b