How do you solve and check for extraneous solutions in #3sqrt(x^2+9)=3#?
This equation doesn't have real solutions.
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