\(\Leftrightarrow2\left(\frac{a+b+c}{abc}\right)=1\Leftrightarrow2\left(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}\right)=1\)
Mà \(a\le b\le c\Rightarrow1\le2\left(\frac{1}{a^2}+\frac{1}{a^2}+\frac{1}{a^2}\right)\)
\(\Rightarrow a^2\le6\Rightarrow\left[{}\begin{matrix}a=1\\a=2\end{matrix}\right.\)
- Với \(a=1\Rightarrow bc=2\left(1+b+c\right)\)
\(\Leftrightarrow bc-2b-2c+4=6\)
\(\Leftrightarrow\left(b-2\right)\left(c-2\right)=6\) (pt ước số cơ bản, bạn tự giải)
- Với \(a=2\Rightarrow2bc=2\left(2+b+c\right)\)
\(\Rightarrow bc-b-c+1=3\Leftrightarrow\left(b-1\right)\left(c-1\right)=3\)
