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If =k , then ( - 2 ) ( + 2 ) is equal to

Options

  1. Ak+1 k-1
  2. Bk-1 k+1
  3. C1-k 1+k
  4. D1+k 1-k

Correct answer

B. k-1 k+1

Step-by-step solution

Given = k , we have = k . Applying componendo and dividendo: + - = k+1 k-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 ) , we get: 2 ( + 2 ) ( - 2 ) 2 ( + 2 ) ( - 2 ) = k+1 k-1 This simplifies to ( + 2 ) ( - 2 ) = k+1 k-1 . Taking the reciprocal of both sides: ( + 2 ) ( - 2 ) = k-1 k+1 . Answer: k-1 k+1

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