The number of real roots of $1 + | e^{x} - 1 | = e^{x} (e^{x} - 2)$

0

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Solution

The correct option is C $1$
$1 + | e^{x} - 1 | = e^{x} (e^{x} - 2)$

For, $x > 0$

$1 + e^{x} - 1 = e^{x} (e^{x} - 2)$

$\Rightarrow e^{x} = 3$

For, $x < 0$

$1 - e^{x} + 1 = e^{x} (e^{x} - 2)$

$\Rightarrow e^{x} = 2$

But $e^{x} = 2$ is not a solution because $x < 0$

Therefore, the number of solutions is $1$
Ans: B

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