Question

Find the value of n so that ( a^n + b^n ) / (a + b) may be the geometric mean between a and b.
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Answer 1

${\huge{\bold{\underline{Answer:-}}}}$

Given,  an+bnan+1+bn+1 may be that Geometric mean between a & b

GM=ab

ab=an+bnan+1+bn+1

(ab)21[an+bn]=an+1+bn+1

a(21+n)b21+a21b(21+n)=an+1+bn+1

a(21+n)[b21−a21]=b(n+21)[b21−a21]

a(21+n)=b21−a21b(n+21)[b21−a21]

a(21+n)=b(n+21)⇒(ba)(21+n)=1

⟹21+n=0

⟹n=2−1