# How do you solve and check for extraneous solutions in #3sqrt(x^2+9)=3#?

##### 1 Answer

#### Answer:

This equation doesn't have real solutions.

#### Explanation:

I would first rearrange it as:

square both sides:

At this point you have a problem: there is no real number that can satisfy this equation: no real number squared can give you a negative value!

On the other hand you could use a different type of number although I am not sure you know it.

You can square root both sides and write your equation as:

You can set

So the solutions for your original equation will be:

Now you can substitute back these two solutions into your original equation and they work (considering that