Given that $$a\neq b$$​ and a, b > 0 and $$\frac{a^{n+2} + b^{n+2}}{a^n + b^n} = ab$$​ then $$n^=$$​​

Correct option is D

​$$\begin{aligned}&\textbf{Given:} \quad \text{Given that } a \ne b \text{ and } a, b > 0, \text{ and} \quad \frac{a^{n+2} + b^{n+2}}{a^n + b^n} = ab \\[10pt]&\textbf{Concept used:} \quad \text{We will solve this question by putting all the values from options in the given equation.} \\[10pt]&\textbf{Solution:} \quad \text{If we put } n = -1 \text{ in the given equation, then we get} \\[5pt]&\frac{a^{-1+2} + b^{-1+2}}{a^{-1} + b^{-1}} = \frac{a + b}{\frac{1}{a} + \frac{1}{b}} = \frac{a + b}{\frac{a + b}{ab}} = \frac{(a + b) ab}{a + b} = ab \\[10pt]&\text{which is our right-hand side.} \\[5pt]&\text{Hence } n = -1.\end{aligned}$$

Final Answer:  -1.