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.