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If the AM and GM between two numbers are in the ratio m: n , then what is the ratio between the two numbers?

Options

  1. Am+ m^2-n^2 m- m^2-n^2
  2. Bm+n m-n
  3. Cm^2-n^2 m^2+n^2
  4. Dm^2+n^2-m n m^2+n^2+m n

Correct answer

A. m+ m^2-n^2 m- m^2-n^2

Step-by-step solution

According to question, aligned & a+b 2 a b = m n & a+b+2 a b a+b-2 a b = m+n m-n aligned (By componendo and devidendo) aligned & ( a + b )^2 ( a - b )^2 = m+n m-n & a + b a - b = m+n m-n & 2 a 2 b = m+n + m-n m+n - m-n aligned (By componendo and devidendo) a b = m+ m^2-n^2 m- m^2-n^2

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