\(a^2+b^2+c^2=ab+bc+ca\)
\(\Leftrightarrow2a^2+2b^2+2c^2-2ab-2ac-2bc=0\)
\(\Leftrightarrow\left(a-c\right)^2+\left(b-c\right)^2+\left(a-b\right)^2=0\)
=>a=b=c
\(A=\left(a+a\right)^2-2\left[\left(b+b-b\right)^2+\left(b+b-b\right)^2\right]\)
\(=4b^2-2\left[b^2+b^2\right]=0\)