# If 2,5 and x,6 are the endpoints of a segment with length √17,what is the value of x ?

Jun 26, 2018

$x = 6$ or $x = - 2$

#### Explanation:

By the Pythagorean Theorem
$\textcolor{w h i t e}{\text{XXX}} \sqrt{{\left(x - 2\right)}^{2} + {\left(6 - 5\right)}^{2}} = \sqrt{17}$

$\textcolor{w h i t e}{\text{XXX}} {\left(x - 2\right)}^{2} + 1 = 17$

$\textcolor{w h i t e}{\text{XXX}} {x}^{2} - 4 x + 4 + 1 - 17 = 0$

$\textcolor{w h i t e}{\text{XXX}} {x}^{2} - 4 x - 12 = 0$

$\textcolor{w h i t e}{\text{XXX}} \left(x - 6\right) \left(x + 2\right) = 0$

So $x = 6$ or $x = - 2$