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??? :)

Printable View

- Oct 5th 2009, 10:11 PMfvaras89Equations
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 PMearboth
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 AMpacman
i let

*y = sqrt(2x+11) - sqrt(2x-5) - 2, see my plot it may help you guess the answer*