Chapter 13, Problem 34E

Consider the quadratic equation $\left(F_{N-2}\right)x^2=\left(F_{N-1}\right)x+F_N$, where $F_{N-2}$, $F_{N-1}$, and $F_N$

are consecutive Fibonacci numbers.

a. Show that $x=-1$ is one of the two solutions of the equation. [Hint: Try Exercises

31(a) or 32(a) first.]

b. Find the second solution of the equation expressed in terms of Fibonacci numbers.

[Hint: Try Exercises 31(b) or 32(b) first.]