Then 4b 2-4ac = 0, 4c 2-4ab = 0, 4a 2-4bc = 0.

That is, b 2 = ca, c 2 = ab and a 2 = BC.

(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)

(a-b)^2+(b-c)^2+(c-a)^2=2(a^2+b^2+c^2)-2(ab+bc+ca)

=0

The contradiction that A, B and C are not equal is true if and only if A = B = C.

So the hypothesis is not true, and the original proposition is true.

This is?

?