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