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

1 Answer
Adrian D.
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>=0 => 6>=x

and

x-6>=0 => x>=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.

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