Respuesta :
Answer: x= 4 is an extraneous solution.
Step-by-step explanation:
Since we have given that
[tex]3(\sqrt{x+5})=-9[/tex]
We need to find the extraneous solution.
So, our equation becomes,
[tex]\sqrt{x+5}=\frac{-9}{3}\\\\\sqrt{x+5}=-3\\\\\text{On squaring both sides}\\\\x+55=(-3)^2\\\\x+5=9\\\\x=9-5\\\\x=4[/tex]
Now, we will check that x = 4 is an extraneous solution.
[tex]3\sqrt{4+5}\neq -9\\\\3\sqrt{9}\neq -9\\\\3\times 3\neq -9\\\\9\neq -9[/tex]
Hence, x= 4 is an extraneous solution.
