Answer: The solution to the above expression is 10.
It is not extraneous solution, as it not satisfying the equation.
Step-by-step explanation:
Since we have given that
3 square root x+6 =-12
that means,
[tex]3\sqrt{x+6}=-12[/tex]
We just need to find the value of x:
[tex]3\sqrt{x+6}=-12\\\\\sqrt{x+6}=\frac{-12}{3}\\\\\sqrt{x+6}=-4\\\\\text{ On squaring both sides, we get}\\\\x+6=(-4)^2\\\\x+6=16\\\\x=16-6\\\\x=10[/tex]
Hence, the solution to the above expression is 10.
Now, we have to check whether it is extraneous solution or not.
Put x= 10 in the above expression,
[tex]3\sqrt{10+6}=-12\\\\3\sqrt{4}=-12\\\\3\times 4=-12\\\\12\neq -12[/tex]
Hence, it is not extraneous solution, as it not satisfying the equation.
