Answer:
To solve the equation, we need to isolate the square root term and square both sides of the equation. We have:
1 + √n + 11 = n
√n = n - 12
Squaring both sides:
n = (n - 12)^2
n = n^2 - 24n + 144
n^2 - 25n + 144 = 0
Factorizing the quadratic equation:
(n - 16)(n - 9) = 0
Therefore, n = 16 or n = 9. We need to check these solutions in the original equation to see if they are valid.
For n = 16:
1 + √16 + 11 = 16
1 + 4 + 11 = 16
16 = 16
The solution n = 16 satisfies the equation.
For n = 9:
1 + √9 + 11 = 9
1 + 3 + 11 = 9
15 = 9
The solution n = 9 does not satisfy the equation.
Therefore, the only real solution is n = 16, which corresponds to option C: -2 is an extraneous solution and 5 is a real solution.
Hope This Helps!