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

If the minimum value of fx=5x22+αx5,x>0, is 14, then the value of α is equal to
  1. 32
  2. 64
  3. 128
  4.  256

Solution

From weighted A.M.-G.M. inequality, we know

5x22+2α2x55+2≥x225·α2x5217

⇒5x22+αx5≥72α27

Given that the least value of 5x22+αx5 is 14

i.e. 72α27=14⇒α17=2⇒α=128

Asked in: JEE Main 2022 (28 Jul Shift 1)

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