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 = (-b \pm √(b^2 - 4ac))/(2a) = (-1 \pm √(1^2 - 4(1)(-1)))/(2) = (-1 \pm \sqrt5)/(2)`
the positive root is special because it's equal to the golden ratio