If $$13 = \frac{{13w}}{{\left( {1 - w} \right)}}$$   , then (2w)² = ?

$$\eqalign{ & \Rightarrow \frac{{13}}{1} = \frac{{13w}}{{\left( {1 - w} \right)}} \cr & \Rightarrow \frac{w}{{\left( {1 - w} \right)}} = 1 \cr & \Rightarrow w = 1 - w \cr & \Rightarrow 2w = 1 \cr & \Rightarrow w = \frac{1}{2} \cr & \therefore {\left( {2w} \right)^2} \cr & = 4{w^2} \cr & = 4 \times \frac{1}{4} \cr & = 1 \cr} $$