$\frac{a^{2}}{a +2b^{3}}$ = $\frac{a( a+2b^{3}) -2ab^{3}}{a + 2b^{3}}$ =a - $\frac{2ab^{3}}{a +2b^{3}}$ a + $2b^{3}$ $\geq$ 3$\sqrt[3]{b^{3}b^{3}a}$ =3 $b^{2}$ $\sqrt[3]{a}$
$\Rightarrow$ $\frac{a^{2}}{a + 2b^{3}}$ $\geq$ a - $\frac{2b\sqrt[3]{a^{2}}}{3}$
TT $\Rightarrow$ B $\geq$ a+b +c- $\frac{2}{3}$ (b $\sqrt[3]{a^{2}}$ +c $\sqrt[3]{b^{2}}$ +a $\sqrt[3]{c^{2}}$ )
cm BT trong ngoặc $\leq$ 3 (co si)
$\Rightarrow$ B $\geq$ 1
dấu '=" $\Leftrightarrow$ a=b=c=1