NDA 2016 Maths · Mathematics · Sequences and Series · easy

For x>0, x+1/x≥2. 2. For x<0, x+1/x≥2.

Single correct option

Consider the following statements:
1. For

x>0

x+\dfrac1x\ge2

.
2. For

x<0

x+\dfrac1x\ge2

.
Which of the statements given above is/are correct?

Show answer and solution

Answer: (A) 1 only

For

x>0

, AM-GM gives

x+\dfrac1x\ge2\sqrt{x\cdot\dfrac1x}=2

, so statement 1 holds. For

x<0

both terms are negative, so the sum is at most

-2

(for example

x=-1

gives

-2

), hence statement 2 is false.

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