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... 

Here is a way
we have :
$$b=\dfrac{1}{3-a}\ \ \  c=\dfrac{1}{4-b}\tag1$$
hence :
$$\dfrac{1}{4-\dfrac{1}{3-a}}+\frac{1}{a}=\frac{3-a}{11-4a}+\frac{1}{a}=\frac{9}{11}$$
so $11((3-a)a-11+4a)=9a(11-4a)$ or $25a^2-110a+121=0$ so $a=\frac{11}{5}$ and here you can find $a$ and repalce in $(1)$ to find $b$ and $c$
