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RRB RPF RPSF SI and CONS Model Papers 3 with solutions

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Question : 13 of 120

Marks: +1, -0

The least value of

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

is :

2
1
0
$\frac{2}{3}$

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

\frac{1}{A} = 3^{-x}

⇒ Both are positive.

Now, A.M. of A and

\frac{1}{A}

is greater than or equal to their G.M.

i.e.

\frac{A + \frac{1}{A}}{2} \ge \sqrt{A \cdot \frac{1}{A}}

or

A + \frac{1}{A} \ge 2

or

3^{x} + 3^{-x} \ge 2

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