Hi,
What rearrangements do you make to find x?:
1/x = x - 2
Apparently the answer is x = 1 + 2^0.5
Please help!
$\displaystyle \frac{1}{x} = x - 2$
$\displaystyle 1 = x^2 - 2x$
$\displaystyle 0 = x^2 - 2x - 1$
$\displaystyle 0 = x^2 - 2x + (-1)^2 - (-1)^2 - 1$
$\displaystyle 0 = (x - 1)^2 - 2$
$\displaystyle 2 = (x - 1)^2$
$\displaystyle \pm \sqrt{2} = x - 1$
$\displaystyle 1 \pm \sqrt{2} = x$.