Find if . (Source: Mandelbrot)
Multiplying both sides by , we get , so . Multiplying by gives , so , and thus .
I think we can do much better than that:
and have symmetric roles in the equation. Thus, if is a solution, so is . Since the questions asks to find , there must be only one value it equals regardless of or . Thus, the sought amount equals its reciprocal, and is thus either 1 or -1. Since the latter causes a zero denominator in the left hand side, the answer must be the only choice left, .