Question

The minimum value of the expression; $a+\frac{1}{a};a>0$is:

• A. -2
• B. 2
• C. 1
• D. can’t be determined

Answer 1

The correct option is B 2

Soln:

$a+\frac{1}{a}={(\sqrt{a}-\frac{1}{\sqrt{a}})}^2+2$

For minimum value of$a+\frac{1}{a}$,we want minimum value of${(\sqrt{a}-\frac{1}{\sqrt{a}})}^2$that will be zero.

So, minimum value of$a+\frac{1}{a}$will be 2. Hence option (b)

2nd method:- By, $A.M\ge G.M\frac{a+\frac{1}{a}}{2}\ge \sqrt{(a\times \frac{1}{a}}thusa+\frac{1}{a}>2(i.e.,)(a+\frac{1}{a})$min will be 2 . option (b).