# If a^{n} + b^{n}/a^{n }^{- }^{1} + b^{n }^{- }^{1} is the A.M between a and b , then find the value of n

**Solution:**

A.M of a and b = (a + b)/2

According to the question,

⇒ (a + b)/2 = (a^{n} + b^{n})/(a^{n }^{- }^{1} + b^{n }^{- }^{1})

⇒ (a + b)(a^{n }^{- }^{1} + b^{n }^{- }^{1})

= 2 (a^{n} + b^{n})

⇒ a^{n} + ab^{n }^{- }^{1} + ba^{n }^{- }^{1} + b^{n} = 2a^{n} + 2b^{n}

⇒ ab^{n }^{- }^{1} + ba^{n }^{- }^{1} = a^{n} + b^{n}

⇒ ab^{n }^{- }^{1} - b^{n} = a^{n} - ba^{n }^{- 1}

⇒ b^{n }^{- }^{1} (a - b) = a^{n }^{- }^{1} (a - b)

⇒ b^{n }^{- }^{1}= a^{n }^{- 1}

(a/b)^{n }^{- }^{1} = 1 = (a/b)(a/b)^{0}

⇒ n - 1 = 0

⇒ n = 1

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.2 Question 15

## If a^{n} + b^{n}/a^{n }^{- }^{1} + b^{n }^{- }^{1} is the A.M between a and b , then find the value of n

**Summary:**

The value of n given that a^{n} + b^{n}/a^{n }^{- }^{1} + b^{n }^{- }^{1} is the A.M between a and b is 1

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