from( 1)a2+B2+C2-A B-BC-CA = 0。
Get ab+BC+ca = a 2+b 2+c 2 > 0(3).
ab+bc+ca=(a+c)b+ca=ca-b^2>； 0(4)
Obtain ca>0, similarly ba>0, bc & gt0,(5)
From this, we can get that the symbols of A, B and C are the same, all positive or all negative!
This is obviously inconsistent with condition (2), so the original formula cannot be proved by the above two conditions!
To put it more simply, you can see from my formula (3) that your fourth step of reasoning is wrong, that is, you can't get ab+bc+ac=0, because they are all greater than 0!