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JEE Main202228 Jul 2022Morning ShiftMathematicsSequences and SeriesActual

If the minimum value of f x = 5 x 2 2 + α x 5 , x > 0 , is 14 , then the value of α is equal to

Options

  1. A32
  2. B64
  3. C128
  4. D  256

Correct answer

C. 128

Step-by-step solution

From weighted A . M . - G . M . inequality, we know 5 x 2 2 + 2 α 2 x 5 5 + 2 ≥ x 2 2 5 · α 2 x 5 2 1 7 ⇒ 5 x 2 2 + α x 5 ≥ 7 2 α 2 7 Given that the least value of 5 x 2 2 + α x 5   is   14 i.e. 7 2 α 2 7 = 14 ⇒ α 1 7 = 2 ⇒ α = 128

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