If $$\frac{x}{a} = \frac{1}{a} - \frac{1}{x}{\text{,}}$$   then the value of x - x² is?

Solution (By Examveda Team)

$$\eqalign{ & \frac{x}{a} = \frac{1}{a} - \frac{1}{x} \cr & \Rightarrow \frac{x}{a} - \frac{1}{a} = - \frac{1}{x} \cr & \Rightarrow \left( {\frac{{x - 1}}{a}} \right) = - \frac{1}{x} \cr & \Rightarrow \frac{{1 - x}}{a} = \frac{1}{x} \cr & \Rightarrow x\left( {1 - x} \right) = a \cr & \Rightarrow x - {x^2} = a \cr} $$