Question

Given the equation 2Square root of x minus 5 = 2, solve for x and identify if it is an extraneous solution.

Answer 1

\(2 \sqrt{x-5} = 2\)

I'd suggest first dividing both sides by 2 and then squaring both sides to get rid of the square root

And then solve for x

An extraneous solution is one that when you plug it back in, it doesn't work so you have to make sure that whatever you got x equals to is an actual solution
We have to do this because we're dealing with square roots


And we can't take the square root of negative numbers so we have to make sure that the solution would not make the inside of it negative

Let me know what you get or if you'd like me to clarify further!