Giải thích các bước giải:
b.Ta có :
$A=\dfrac{a^2}{b+c}+\dfrac{b^2}{c+a} +\dfrac{c^2}{a+b}$
$A((b+c)+(c+a)+(a+b))=(\dfrac{a^2}{b+c}+\dfrac{b^2}{c+a} +\dfrac{c^2}{a+b})((b+c)+(c+a)+(a+b))$
$A((b+c)+(c+a)+(a+b))\ge (\sqrt{\dfrac{a^2}{b+c}.(b+c)}+\sqrt{\dfrac{b^2}{a+c}.(a+c)}+\sqrt{\dfrac{c^2}{a+b}.(a+b)})^2$
$A(2(a+b+c))\ge (a+b+c)^2$
$A\ge\dfrac{ a+b+c}{2}$