NDA 2016 Maths · Mathematics · Sequences and Series · medium

For x>0, the minimum value of 4x+9/x+5 is

Single correct option

For

x>0

, the minimum value of

4x+\dfrac9x+5

Show answer and solution

Answer: (D) $17$

By AM-GM,

4x+\dfrac9x\ge2\sqrt{4x\cdot\dfrac9x}=2\sqrt{36}=12

, with equality when

4x=\dfrac9x

, i.e.

x=\tfrac32

. Adding the constant 5 gives the minimum

17

. The value 12 forgets the constant term.

Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake