How do you solve sqrt(6-x)-sqrt(x-6)=2  and find any extraneous solutions?

Dec 23, 2016

The set of feasible solutions is $\left(6 - x \ge 0\right) \cap \left(x - 6 \ge 0\right)$ which is precisely $x = 6$. But putting $x = 6$ into the equation we obtain
$0 = 2$