Find the solution of 3 times the square root of the quantity of x plus 5 equals negative 9, and determine if it is an extraneous solution.
Answer: x= 4 is an extraneous solution.
Step-by-step explanation:
Since we have given that
\(3(\sqrt{x+5})=-9\)
We need to find the extraneous solution.
So, our equation becomes,
\(\sqrt{x+5}=\frac{-9}{3}\\\\\sqrt{x+5}=-3\\\\\text{On squaring both sides}\\\\x+55=(-3)^2\\\\x+5=9\\\\x=9-5\\\\x=4\)
Now, we will check that x = 4 is an extraneous solution.
\(3\sqrt{4+5} eq -9\\\\3\sqrt{9} eq -9\\\\3\times 3 eq -9\\\\9 eq -9\)
Hence, x= 4 is an extraneous solution.