Answer:
C.The solution n = 0 is an extraneous solution.
Step-by-step explanation:
The given equation is [tex]\sqrt{n+4} =n-2.[/tex]
Squaring both sides we have:
[tex]n+4=(n-2)^{2}[/tex]
Expanding the right side:
[tex]n+4=n^{2} -4n+4[/tex]
Or ,
[tex]n^{2} -5n=0[/tex]
n(n-5)=0
n=0 or n=5.
Checking the solution for n=0 in the above equation:
[tex]\sqrt{0+4} =0-2[/tex] False .
For n=5.
[tex]\sqrt{5+4} =5-2[/tex]
True.
C.The solution n = 0 is an extraneous solution.
