Question

Solve 1/x = x - 1 What is special about the positive solution?

Answer 1

1 = x^2 - x
x^2-x-1=0
quadratic formula:
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-1 \pm \sqrt{1^2 - 4(1)(-1)}}{2} = \frac{-1 \pm \sqrt5}{2}$
the positive root is special because it's equal to the golden ratio