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( 12 - 12 ) ( 12 + 12 )=

Options

  1. A2
  2. B2 2
  3. C4 2
  4. D1 2

Correct answer

B. 2 2

Step-by-step solution

Let x = 12 . The expression is ( x - x)( x + x) . We know that x + x = x x + x x = ^2 x + ^2 x x x = 1 x x . Multiplying by 2 in the numerator and denominator, we get 2 2 x x = 2 2x . Substituting x = 12 , 2x = 6 . Thus, x + x = 2 ( /6) = 2 1/2 = 4 . Now consider the first term: x - x . Using the identity x - x = 2 ( 1 2 x - 1 2 x ) = 2 (x + /4) . For x = /12 , x + /4 = /12 + 3 /12 = 4 /12 = /3 . So, ( /12) - ( /12) = 2 ( /3) = 2 1 2 = 1 2 . The product is 1 2 4 = 4 2 = 2 2 . Answer: 2 2

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