# algebra equation

• Sep 28th 2008, 03:50 PM
jcube69
algebra equation
$\displaystyle \sqrt{x+a} + \sqrt{x - a} = \sqrt{2} \sqrt{x+7}$

i need it simplified (it is multiple choice) but as much as i may try i cant rember how to do this type of problem plz help thank you.

if u want the 5 choices i have..i can give them...but it owuld do no good because i still want to know how to solve the problem (show the work if you can)
• Sep 28th 2008, 04:03 PM
Prove It
Quote:

Originally Posted by jcube69
i have no idea how to make a radical around somthing so ill do my best and place # where the radical begins -.-

#(x+a) + #(x-a)=#2*#(x+7)

i need it simplified (it is multiple choice) but as much as i may try i cant rember how to do this type of problem plz help thank you.

if u want the 5 choices i have..i can give them...but it owuld do no good because i still want to know how to solve the problem (show the work if you can)

So are you trying to solve this equation...

$\displaystyle \sqrt{x+a} + \sqrt{x - a} = \sqrt{2} \sqrt{x+7}$ ???

P.S. the code is, after you've written math in square brackets,
sqrt{expression under square root sign}, and then write /math in square brackets.
• Sep 28th 2008, 04:05 PM
jcube69
yes exactly how it is
• Sep 28th 2008, 04:38 PM
Prove It
Quote:

Originally Posted by Prove It
So are you trying to solve this equation...

$\displaystyle \sqrt{x+a} + \sqrt{x - a} = \sqrt{2} \sqrt{x+7}$ ???

P.S. the code is, after you've written math in square brackets,
sqrt{expression under square root sign}, and then write /math in square brackets.

$\displaystyle \sqrt{x+a} + \sqrt{x - a} = \sqrt{2} \sqrt{x+7}$

Squaring both sides gives

$\displaystyle x + a + 2\sqrt{x+a}\sqrt{x-a} + x - a = 2(x+7)$

$\displaystyle 2x + 2\sqrt{(x+a)(x-a)} = 2x + 14$

$\displaystyle 2\sqrt{x^2 - a^2} = 14$

$\displaystyle \sqrt{x^2 - a^2} = 7$

$\displaystyle x^2 - a^2 = 49$

$\displaystyle x^2 = a^2 + 49$

$\displaystyle x = \pm \sqrt{a^2 + 49}$.
• Sep 28th 2008, 04:48 PM
jcube69
thank you very much

i ahd the right idea but did a step wrong ^.^

thanks again^.^