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Let $S$ be the set of all real roots of the equation, $3^{x} (3^{x} - 1) + 2 = | 3^{x} - 1 | + | 3^{x} - 2 |$ . Then $S$ is

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is an empty set

Contains exactly two elements

Contains at least four elements

is a singleton

answer is A.

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Detailed Solution

$L e t 3^{x} = t$

$t (t - 1) + 2 = | t - 1 | + | t - 2 |$

$t = a$

$3^{x} = a$

$x = \log_{3} a so singleton set$

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