Giải thích các bước giải:
Ta có:
$A=a+\dfrac{27}{2(a-1)(a+1)^3}$
$\to A=\dfrac12a+(\dfrac{27}{2(a-1)(a+1)^3}+\dfrac12(a-1)+\dfrac12)$
$\to A\ge \dfrac12a+3\sqrt[3]{(\dfrac{27}{2(a-1)(a+1)^3}\cdot \dfrac12(a-1)\cdot \dfrac12}$
$\to A\ge \dfrac12a+\dfrac9{2(a+1)}$
$\to A\ge \dfrac12(a+1)+\dfrac9{2(a+1)}-\dfrac12$
$\to A\ge 2\sqrt{\dfrac12(a+1)\cdot\dfrac9{2(a+1)}}-\dfrac12$
$\to A\ge 3-\dfrac12$
$\to A\ge \dfrac52$
Dấu = xảy ra khi $a=2$
