Minimum value of the expresssion $3^{2 x} + 3^{- 2 x}$ is

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Solution

$3^{2 x} + 3^{- 2 x} = 3^{2 x} + \frac{1}{3^{2 x}}$
Since it is in the form of $x + \frac{1}{x}$ and $3^{2 x} > 0, \forall x \in R$ ,
then minimum value of $3^{2 x} + 3^{- 2 x}$ is $2$

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