Question

if p^n+1+q^n+1/p^n+q^n is the AM of p and q. then, n will be​

Answer 1

Step-by-step explanation:

APQ:

$\frac{ {p}^{n + 1} + {q}^{n + 1} }{ {p}^{n} + {q}^{n} } = \frac{p + q}{2}$

$2 {p}^{n + 1} + 2 {q}^{n + 1} = ( {p}^{n} + {q}^{n} )(p + q)$

${p}^{n + 1} + {q}^{n + 1} = p {q}^{n} + q {p}^{n}$

${p}^{n + 1} - q {p}^{n} + {q}^{n + 1} - p {q}^{n} = 0$

${p}^{n} (p - q) - {q}^{n} (p - q) = 0$

$( {p}^{n} - {q}^{n} )(p - q) = 0$

so, we get

${p}^{n} - {q}^{n } = 0$

and

$p - q = 0$

these simply indicate

$p = q$

so, in this case, n can be any real number.

hope this helps you...