### Why do this
problem?

This problem introduces the Golden Ratio as the solution of a
quadratic equation and links to many other investigations. A
solution to the equation can be found by trial and error.

### Possible approach?

To motivate the topic why not introduce several problems where the
students can discover that the Golden Ratio occurs in very
different contexts and reinforce their own understanding of the
algebra that occurs. For example:

Golden Powers ,

Golden Triangle and

Golden Eggs.
### Key questions

If $\phi $ is the golden ratio then what is $\phi^2$ and $1 +
{1\over \phi}$ and does this suggest a way to simplify the final
equation?

### Possible support and
extension

Try the

Golden Trail.