## Intermediate Algebra for College Students (7th Edition)

$8$
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 $x=8$.