Answer
$\{27\}$
Work Step by Step
Step 1. Given the equation as $\sqrt {2x-5}=2+\sqrt {x-2}$
Step 2. Take square on both sides to get: $2x-5=4+4\sqrt {x-2}+x-2$ or $x-7=4\sqrt {x-2}$
Step 3. Take square on both sides again to get: $x^2-14x+49=16x-32$ or $x^2-30x+81=0$ which gives $x=3,27$
Step 4. Check answer in the original equation: only $\{27\}$ fits.
