Write the solution set of the inequation x^2 x-2 >0 - Vidyadip

Question

Write the solution set of the inequation $\frac{\text{x}^2}{\text{x}-2}>0$

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Answer

We have

$\frac{\text{x}^2}{\text{x}-2}>0$

$\Rightarrow\text{x}-2\geq0$ $\Big[\because\frac{\text{a}}{\text{b}}>0$ and $\text{a}>0\Rightarrow\text{b}\geq0\Big]$

$\Rightarrow\text{x}\geq2 $

$\Rightarrow\text{x}\in[2,\infty)$

Hence, the solution set of the given inequation is $[2,\infty)$

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