A simultaneous system of equations Solve for $a,b,c$:
\begin{align}
2ab+a+2b=24\\
2bc+b+c=52\\
2ac+2c+a=74\\
\end{align}
Solving them simultaneously is leading to very difficult situation. Plz help.

\begin{align}
(a+1)(2b+1)&=(2ab+a+2b)+1=25\\
(2b+1)(2c+1)&=2(bc+b+c)+1=105\\
(2c+1)(a+1)&=(2ca+2c+a)+1=75
\end{align}
So put $u=a+1,v=2b+1,w=2c+1$ and I think you'll get the answer. (Hint: consider $u^2=(uv)(uw)/(vw)$, et cetera)
