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If A=m B and ( A+B 2 )= ( B-A 2 ) , then is equal to

Options

  1. ANone of these
  2. Bm m-1
  3. Cm+1 m-1
  4. Dm+1 m

Correct answer

C. m+1 m-1

Step-by-step solution

Given A = m B , we have A B = m . Applying componendo and dividendo, A + B A - B = m+1 m-1 . Using the sum-to-product formulas, A + B = 2 ( A+B 2 ) ( A-B 2 ) and A - B = -2 ( A+B 2 ) ( A-B 2 ) . Substituting these into the ratio, 2 ( A+B 2 ) ( A-B 2 ) -2 ( A+B 2 ) ( A-B 2 ) = m+1 m-1 . This simplifies to - ( A+B 2 ) ( A-B 2 ) = m+1 m-1 . Since ( A-B 2 ) = 1 ( A-B 2 ) = 1 - ( B-A 2 ) , we have - ( A+B 2 ) ( - 1 ( B-A 2 ) ) = m+1 m-1 . Therefore, ( A+B 2 ) = m+1 m-1 ( B-A 2 ) . Comparing this with the given equation

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