# How do you solve and check for extraneous solutions in sqrt(6-x)-sqrt(x-6)=2?

Aug 3, 2015

There are no real valued solutions to the equation.

#### Explanation:

First note that the expressions in the square roots must be positive (restricting to real numbers). This gives the following constraints on the value of $x$:

$6 - x \ge 0$ => $6 \ge x$

and

$x - 6 \ge 0$ => $x \ge 6$

$x = 6$ is the only solution to these inequalities. $x = 6$ does not satisfy the equation in the question, therefore there are no real valued solutions to the equation.