Answer
$8$
Work Step by Step
Simplify. $ (\sqrt{x-4}+\sqrt {x+1})=5$
Take square on both sides.
we have, $ (\sqrt{x-4}+\sqrt {x+1})^2=5^2$
or, $(x-4)^2+(x+1)^2+2 (\sqrt{x-4}+\sqrt {x+1})=25$
or, $2x-28=-2 (\sqrt{x-4}+\sqrt {x+1})$
Thus, $x^2-28x+196=x^2-3x-4$
$-25x=-200$
Hence, we can conclude that $x=8$.
