# Find all real solutions- Please help

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• Mar 31st 2009, 08:59 AM
aperkin2
Find all real solutions- Please help
Hi! I was working on my homework and got stuck!

My problem says to "Find all real solutions for-

square root of (x+3) plus the square root of (xt8) = 1

I know that I need to isolate a radical first so I did-

square root of (x+3) = 1 minus square root of (x+8)

And then I think I need to square both sides, but I'm not sure where to go from there.

Thanks for your help (in advance!)

Ashley
• Mar 31st 2009, 09:50 AM
HallsofIvy
Quote:

Originally Posted by aperkin2
Hi! I was working on my homework and got stuck!

My problem says to "Find all real solutions for-

square root of (x+3) plus the square root of (xt8) = 1

I know that I need to isolate a radical first so I did-

square root of (x+3) = 1 minus square root of (x+8)

And then I think I need to square both sides, but I'm not sure where to go from there.

Thanks for your help (in advance!)

Ashley

Yes, square both sides of that to get $\displaystyle x+ 3= 1- 2\sqrt{x+8}+ x+ 8$ which can be simplified to $\displaystyle 2\sqrt{x+ 8}= 6$. Now square again. Be sure to check your solution in the original equation. It is quite possible that a problem like this does not have a solution.