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AP EAMCET201923 Apr 2019Morning ShiftMathematicsLimitsActual

If ( _ x 0 [(a-n) n x- x] n x x^2 =0,(n 0) ) then the minimum possible positive value of (a ) is

Options

  1. A0
  2. B-2
  3. C2
  4. D1

Correct answer

C. 2

Step-by-step solution

( aligned & _ x 0 ((a-n) n x- x) n x x^2 =0, n 0 & _ x 0 ( (a-n) n x x - x x ) (n x) x =0 & [ _ x 0 n x n x =n ] & n (a n-n^2-1 )=0 a=n+ 1 n , n 0 & n+ 1 n 2 n 1 n (by AM GM) & a 2 1 & a 2 aligned ) ( ) Minimum possible positive value of (a ) is 2. Hence, option (c) is correct.

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