A=\frac{a^{2}}{ba+ca}+\frac{b^{2}}{bc+ab}+\frac{c^{2}}{bc+ac}\Rightarrow A\times \left ( ab+bc+ca \right )\geqslant \left ( a+b+c \right )^{2}\Rightarrow A\geqslant \frac{a^{2}+b^{2}+c^{2}+2ab+2bc+2ca}{2ab+2bc+2ca}\geqslant \frac{3}{2}vi:a^{2}+b^{2}+c^{2}\geqslant ab+bc+ca
$A=\frac{a^{2}}{ba+ca}+\frac{b^{2}}{bc+ab}+\frac{c^{2}}{bc+ac}
$$\Rightarrow A\times \left ( ab+bc+ca \right )\geqslant \left ( a+b+c \right )^{2}
$$\Rightarrow A\geqslant \frac{a^{2}+b^{2}+c^{2}+2ab+2bc+2ca}{2ab+2bc+2ca}\geqslant \frac{3}{2}
$vi:
$a^{2}+b^{2}+c^{2}\geqslant ab+bc+ca
$