Question about a solution of a system of three non linear equations in three unknowns Let $a$, $b$ and $c$ be positive real numbers such that $$ a + \frac{1}{b} = 3$$  $$b + \frac{1}{c} = 4$$ $$ c + \frac{1}{a} = \frac{9}{11} $$ then $$ a \times b \times c  =?$$ 
I tried doing this problem but I was unsuccessful. Tried a lot but couldn't get the answer! The answer is a numerical value... 


Let $a$, $b$ and $c$ be positive real numbers such that 

\begin{align}
a + \frac{1}{b} &= 3 \tag{1}\label{1}
\\
b + \frac{1}{c} &= 4  \tag{2}\label{2}
\\
c + \frac{1}{a} &= \frac{9}{11} \tag{3}\label{3}
\end{align}
\eqref{1}$\times$\eqref{2}$\times$\eqref{3}
$-$\eqref{1}$-$\eqref{2}$-$\eqref{3} gives:
\begin{align}
abc+\frac{1}{abc}&=2,
\end{align}
hence $abc=1$.
