I kind of hate problems where the solution is to find the most elegant answer possible. This problem is an excellent example of why. My solution (here), solves the problem as stated – but I took a grinder solution just wearing the problem away. My gut says that there is no way that this is the solution they want – however I do solve it with multiple applications of the quadratic equation, which the problem framing hinted at, so I am posting it for now.
Knowing that this is not the solution they wanted, I want to go look at the back of the book to confirm that is the case, and see what they were after. The problem with looking though is that I ruin the problem. So, I pretty much never want to look – hence my dislike of problems I where I can not prove I have the right solution. They all seem to be asking me to prove that someone smarter than I am could not solve the problem in a more elegant manner, but since the person in question is by definition smarter than I am – well – it seems a might ridiculous.
Here we have the problem:
“Solve this equation using nothing higher tan quadratic equations:
X = Sqrt( (X-(1/X)) + Sqrt(1-(1/X)) )”