Question

if n=2+√3 find the value of n+1/b​

Answer 1

Answer:

Given,

a

n

+b

n

a

n+1

+b

n+1

may be that Geometric mean between a & b

GM=

ab

ab

=

a

n

+b

n

a

n+1

+b

n+1

(ab)

2

1

[a

n

+b

n

]=a

n+1

+b

n+1

a

(

2

1

+n)

b

2

1

+a

2

1

b

(

2

1

+n)

=a

n+1

+b

n+1

a

(

2

1

+n)

[b

2

1

−a

2

1

]=b

(n+

2

1

)

[b

2

1

−a

2

1

]

a

(

2

1

+n)

=

b

2

1

−a

2

1

b

(n+

2

1

)

[b

2

1

−a

2

1

]

a

(

2

1

+n)

=b

(n+

2

1

)

⇒(

b

a

)

(

2

1

+n)

=1

⟹

2

1

+n=0

⟹n=

2

−1

Answer 2

Answer:

$n + \frac{1}{b} \\ = 2 + \sqrt{3} + \frac{1}{b} \\ = \frac{2b + \sqrt{3}b + 1 }{b(2 + \sqrt{3)} }$

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