Answer
The extraneous solution is $y=-1$.
Work Step by Step
The given equation is
$\Rightarrow \sqrt{2y+3}=y$
Check $y=-1$.
$\Rightarrow \sqrt{2y+3}=y$
$\Rightarrow \sqrt{2(-1)+3}=-1$
$\Rightarrow \sqrt{-2+3}=-1$
$\Rightarrow \sqrt{1}=-1$
$\Rightarrow 1=-1$
False.
Check $y=3$.
$\Rightarrow \sqrt{2y+3}=y$
$\Rightarrow \sqrt{2(3)+3}=3$
$\Rightarrow \sqrt{6+3}=3$
$\Rightarrow \sqrt{9}=3$
$\Rightarrow 3=3$
True.
Hence, the extraneous solution is $y=-1$.
