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The least value of a in RR for which 4a...

The least value of `a in RR` for which `4ax^2+1/x >= 1`, for all `x > 0`, is

A

`(1)/(64)`

B

`(1)/(32)`

C

`(1)/(27)`

D

`(1)/(25)`

Text Solution

Verified by Experts

The correct Answer is:
C
Using A.M.`ge` G.M.
`(4ax^2+(1)/(2x)+(1)/(2x))/(3)ge 3sqrt(4ax^2.(1)/(4x^2))`
`rArr 4ax^2+(1)/(x)ge3 3sqrt(alpha)`
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CENGAGE PUBLICATION-INEQUALITIES INVOLVING MEANS -Jee Advanced (Single
  1. The least value of a in RR for which 4ax^2+1/x >= 1, for all x > 0, ...

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