SOLUTION: Let a be a real number such that a - \frac{1}{a} = 1. Compute a^3.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Let a be a real number such that a - \frac{1}{a} = 1. Compute a^3.      Log On


   



Question 1209401: Let a be a real number such that a - \frac{1}{a} = 1. Compute a^3.
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

Reduce the given equation to the standard form quadratic equation

    a^2 - a - 1 = 0.


Solve it using the quadratic formula.


The roots are  a%5B1%5D = %281+%2B+sqrt%285%29%29%2F2  and  a%5B2%5D = %281+-+sqrt%285%29%29%2F2.


Raise each root to degree 3, performing routine arithmetic.


You will obtain two values/expressions for "a^3".

Boldly go forward following my instructions.