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BITSAT2014MathematicsSequences and SeriesActual

If 1 a , 1 ~b , 1 c are in A. P., then ( 1 a + 1 ~b - 1 c ) ( 1 b + 1 c - 1 a ) is equal to

Options

  1. A4 a c - 3 b²
  2. Bb²-a c a² b² c²
  3. C4 a c - 1 b²
  4. DNone of these

Correct answer

A. 4 a c - 3 b²

Step-by-step solution

1 a - 1 ~b = 1 ~b - 1 c ( 1 a + 1 ~b - 1 c ) ( 1 ~b + 1 c - 1 a )= ( 2 a - 1 ~b ) ( 2 c - 1 ~b )= 4 ac - 1 ~b ( 2 a + 2 c )+ 1 ~b ² = 4 ac - 2 ~b ( 2 ~b )+ 1 ~b ² = 4 ac - 3 ~b ²

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