RRB RPF RPSF SI and CONS Model Papers 3 with solutions

© examsiri.com

Question : 13 of 120

Marks: +1, -0

The least value of

3 ^ { x } + 3 ^ { - x }

is :

2
1
0
$2/3$

Solution:

(a) Working with the options, for x = 0, the least value of

f ( x ) = 3 ^ { x } + 3 ^ { - x } = 2

Alternate :
Let

A = 3 ^ { x }

and

{ 1 }/ { A } = 3 ^ { - x }

⇒ Both are positive.
Now, A.M. of A and

1/\A

is greater than or equal to their G.M.
i.e.

{ A + { 1 }/ { A } }/ { 2 } ≥√{ A . { 1 }/ { A } }

or

A + { 1 }/{ A } ≥ 2

or

3 ^ { x } + 3 ^ { - x } ≥ 2

© examsiri.com

Go to Question:

Prev Question

Next Question