The number of solution of the equation $e^{2 x} + e^{x} + e^{- 2 x} + e^{- x} = 3 (e^{- 2 x} + e^{x})$ is

0

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2

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1

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More than

2

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Solution

The correct option is C $1$
Consider the given equation.
$e^{2 x} + e^{- 2 x} + e^{x} + e^{- x} = 3 e^{- 2 x} + 3 e^{x}$
$e^{4 x} + 1 + e^{3 x} + e^{x} = 3 + 3 e^{3 x}$
$e^{3 x} (e^{x} - 2) + 1 (e^{x} - 2) = 0 (e^{3 x} + 1) (e^{x} - 2) = 0$

Here, $e^{3 x} + 1 = 0$
$e^{3 x} = - 1$
This is not possible, so, this can't be the solution of the given equation.

$e^{x} - 2 = 0 e^{x} = 2 x = ln 2$

So, there is only one solution of this equation.

Hence, option c is the correct option.

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