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If the coefficient of x 7 in ax 2 + 1 bx 1 1 is equal to the coefficient of x - 7 in ax - 1 bx 2 1 1 , then a and b satisfy the relation

Options

  1. Aab = 1
  2. Ba b = 1
  3. Ca + b = 1
  4. Da − b = 1

Correct answer

A. ab = 1

Step-by-step solution

In the expansion of ax 2 + 1 bx 1 1 T r + 1 = 1 1 C r ax 2 1 1 - r 1 bx r = 1 1 C r a 1 1 - r b r · x 2 2 - 3 r For the coefficient of x 7 , put 22 - 3 r = 7 ⇒ r = 5 ∴ T 6 = 1 1 C 5 a 6 b 5 · x 7 ∴ Coefficient of x 7 in the expansion of ax 2 + 1 bx 1 1 is 1 1 C 5 a 6 b 5 Similarly, the coefficient of x - 7 in the expansion ax − 1 bx 2 11 is 11 C 6 a 5 b 6 Now, 1 1 C 5 a 6 b 5 = 1 1 C 6 a 5 b 6 ⇒ a b = 1

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