# A number less its reciprocal is 8/3. What is the number?

Jan 29, 2016

I got two values:
${x}_{1} = 3$
${x}_{2} = - \frac{1}{3}$

#### Explanation:

Let us call our number $x$. We get:
$x - \frac{1}{x} = \frac{8}{3}$
rearranging:
$3 {x}^{2} - 3 = 8 x$
$3 {x}^{2} - 8 x - 3 = 0$
${x}_{1 , 2} = \frac{8 \pm \sqrt{64 + 36}}{6} = \frac{8 \pm 10}{6}$
${x}_{1} = 3$
${x}_{2} = - \frac{1}{3}$