Giải thích các bước giải:
$\text{Đặt a-1=x, b-1=y, c-1=z }\\
\rightarrow A=\dfrac{(x+1)^2}{y}+\dfrac{(y+1)^2}{z}+\dfrac{(z+1)^2}{x}\\
\rightarrow A=\dfrac{x^2+2x+1}{y}+\dfrac{y^2+2y+1}{z}+\dfrac{z^2+2z+1}{x}\\
\rightarrow A=(\dfrac{x^{2}}{y}+\dfrac{1}{y}+\dfrac{y^{2}}{z}+\dfrac{1}{z}+\dfrac{z^{2}}{x}+\dfrac{1}{x})+2(\dfrac{x}{y}+\dfrac{y}{z}+\dfrac{x}{x})\\
\rightarrow A\geq 6\sqrt[6]{\dfrac{x^{2}}{y}.\dfrac{1}{y}.\dfrac{y^{2}}{z}.\dfrac{1}{z}.\dfrac{z^{2}}{x}.\dfrac{1}{x}}+2.3\sqrt[3]{\dfrac{x}{y}.\dfrac{y}{z}.\dfrac{x}{x}}\\
\rightarrow A\geq 12$
