JEE MainMathematicsToughInequalities and absolute value

The number of positive integral values of x satisfying the
inequality
$\frac{\left( 3^{x} - 5^{x} \right)(x - 2)}{\left( x^{2} + 5x + 2 \right)} \geq 0$
is

Show answer and solution

\frac{\left( 3^{x} - 5^{x} \right)(m - 2)}{x^{2} + 5x + 2} \geq 0

For

x > 0\;

3^{x} - 5^{x} < 0 \Rightarrow - ve\

x + 5x + 2 > 0 \Rightarrow + ve

\Rightarrow x - 2 \leq 0

\Rightarrow x \leq 2

\Rightarrow x \in (0,2\rbrack

Integer values = 1, 2

Source: Grass-G / M-05 Mathematics Paper 10 October.docx

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