2014/087) Solve $\sqrt{x-2}- \sqrt{x-7}=1$

Solution

we are given


$\sqrt{x-2}- \sqrt{x-7}=1\cdots (1)$

we have $(x-2) - (x-7) = 5\cdots(2)$

dividing we get

$\sqrt{x-2}+ \sqrt{x-7}=5\cdots (3)$
adding (1) and (3)

$2\sqrt{x-2}=6$
or  $\sqrt{x-2}=3$
or x= 11