Answer
no solution
Work Step by Step
Squaring both sides of the given equation, $
\sqrt{y+5}=2-\sqrt{y-4}
,$ results to
\begin{array}{l}\require{cancel}
(\sqrt{y+5})^2=(2-\sqrt{y-4})^2
\\
y+5=(2)^2-2(2)(\sqrt{y-4})+(\sqrt{y-4})^2
\\
y+5=4-4\sqrt{y-4}+y-4
\\
y+5=y-4\sqrt{y-4}
\\
y-y+5=-4\sqrt{y-4}
\\
5=-4\sqrt{y-4}
\\
\dfrac{5}{-4}=\sqrt{y-4}
\\
\sqrt{y-4}=-\dfrac{5}{4}
.\end{array}
The radical expression at the left side of the equation above reults to a nonnegative number. This will never be equal to the negative expression at the right. Hence, there is $\text{
no solution
}.$
