Radical help

[Pikachuthscoot]

Hello, I just a need a bit of help understading how to do this problem: √ (2x+3)+√ (4-x) = 4

Thanks in advance.

 

[MarkFL]

Hello, and welcome to FMH!

I think I would arrange as:

[MATH]\sqrt{2x+3}=4-\sqrt{4-x}[/MATH]
What do you get when you square both sides? What potential issue do we need to keep in mind in doing so?

 

[Steven G]

You never want to square both sides of an equation that has two square roots on one side as it gets too messy.

So bring one of the square roots to the other side and then square both sides. See where you can get from there.

BTW, we do not solve problems for students on this website as that would not be helping them. We prefer that the student solves their own problem with our help. So in the future you need to show us your work so that we know where you need help.

 

[Pikachuthscoot]

Thank you both, and I will keep that in mind Jomo.

 

[topsquark]

Thank you both, and I will keep that in mind Jomo.

Another point: When you get to your final answer(s) you will want to check them in the original equation. When you square both sides of an equation you have the potential to introduce "extra solutions" that don't actually work. (This is related to the concept that [math](-x)^2 = (x)^2 = |x|^2[/math]. You have to make sure that both your -x and +x are solutions to your original equation.)

-Dan