Answer
$x=16$
Work Step by Step
Simplify. $ (\sqrt{x+9}-\sqrt {x-7})=2$
Take square on both sides.
we have, $ (\sqrt{x+9}-\sqrt {x-7})^2=2^2$
or, $(x+9)^2+(x-7)^2+2 (\sqrt{x+9}+\sqrt {x-7})=4$
or, $2x-2=-2 (\sqrt{x+9}+\sqrt {x -7})$
Thus, $x^2-2x+1=x^2+2x-63$
$-4x=-64$
Hence, we can conclude that $x=16$.
