How do you solve 1/x + 1 = x/2?

Jul 4, 2016

Solns. are $x = 1 \pm \sqrt{3.}$

Explanation:

Given Eqn. $: \frac{1}{x} + 1 = \frac{x}{2}$

Multiplying throughout by $2 x$, eqn. becomes, $2 + 2 x = {x}^{2}$
$\therefore {x}^{2} - 2 x = 2.$

Adding $1$ in both sides, ${x}^{2} - 2 x + 1 = 2 + 1 ,$ or, ${\left(x - 1\right)}^{2} = 3$

$\therefore x - 1 = \pm \sqrt{3}$, i.e., $x = 1 \pm \sqrt{3} ,$ are the reqd. solns.