Solution 17.

The equation     can be written as   

                    ,   

and this quadratic equation has, at most, two distinct solutions:

                       
                    
                    and   
                    
                    .      

We are done.   

Aside.  We can let Mathematica double check our work.

And we can substitute   into the formula  .  

And we can substitute   into the formula  .  

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell