Answer
The extraneous solution is $p=4$.
Work Step by Step
The given equation is
$\Rightarrow \sqrt{12p+16}=-2p$
Check $p=-1$.
$\Rightarrow \sqrt{12p+16}=-2p$
$\Rightarrow \sqrt{12(-1)+16}=-2(-1)$
$\Rightarrow \sqrt{-12+16}=2$
$\Rightarrow \sqrt{4}=2$
$\Rightarrow 2=2$
True.
Check $p=4$.
$\Rightarrow \sqrt{12p+16}=-2p$
$\Rightarrow \sqrt{12(4)+16}=-2(4)$
$\Rightarrow \sqrt{48+16}=-8$
$\Rightarrow \sqrt{64}=-8$
$\Rightarrow 8=-8$
False.
Hence, the extraneous solution is $p=4$.
