Can anyone help me in solving this equation ?? I found it in the chapter of Quadratic equations.....but I have failed to solve it with the methods I know ....Can anyone please help ?
$\displaystyle x = \sqrt{a-\sqrt{a+x}} $
1. The general way to solve equations with square-roots is:
square - isolate remaining square-roots on one side - square - isolate remaining square-roots on one side - square - isolate remaining square-roots on one side - square .... until there is no square-root left.
2. You'll get finally a quadratic equation in a. Solve for a.
3. Afterwards solve these 2 equations for x.
4. Since you may transform a false equation into a true one by squaring you must check if your results satisfy the given original equation.