# Equations

• Oct 5th 2009, 10:11 PM
fvaras89
Equations
Find all real solutions for

sqrt(2x+11) - sqrt(2x-5) = 2

Im not sure of how to do this question.. could someone help pleasee??? :)
• Oct 5th 2009, 10:42 PM
earboth
Quote:

Originally Posted by fvaras89
Find all real solutions for

sqrt(2x+11) - sqrt(2x-5) = 2

Im not sure of how to do this question.. could someone help pleasee??? :)

1. Determine the domain. With your question $\displaystyle x \geq \frac52$

2. Isolate the roots:

$\displaystyle \sqrt{2x+11} = 2+\sqrt{2x-5}$

3. Square both sides:

$\displaystyle 2x+11 = 4+ 2 \cdot 2 \cdot \sqrt{2x-5} +2x-5$

4. Isolate the root .... square both sides of the equation ... isolate the root ... etc until there aren't any roots left. You finally get:

$\displaystyle 9 = 2x-5$

Solve for x.

5. Since squaring is not an equivalent transformation you must check if you got a valid solution: Plug in the value for x into the original equation and check if you get a true statement.
• Oct 6th 2009, 07:07 AM
pacman
i let y = sqrt(2x+11) - sqrt(2x-5) - 2, see my plot it may help you guess the answer