Write the solution set of the inequation x+1 x 2 - Vidyadip

Question

Write the solution set of the inequation $\text{x}+\frac{1}{\text{x}}\geq2$

✓

Answer

We have

$\text{x}+\frac{1}{\text{x}}\geq2$

$\Rightarrow\frac{\text{x}^2+1}{\text{x}}\geq2$

This is only possible if $\text{x}\in(0,\infty)$

$\therefore\text{x}\in[0,\infty)$

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