Question

The set of solutions for $x+\frac{1}{x}\ge 2$ is

• A. $[0,\infty )$
• B. $(0,\infty )$
• C. $[1,\infty )$
• D. $(1,\infty )$

Answer 1

The correct option is B $(0,\infty )$

$x+\frac{1}{x}\ge 2\Rightarrow x+\frac{1}{x}-2\ge 0\Rightarrow \frac{x^2-2x+1}{x}\ge 0\Rightarrow \frac{(x-1{)}^2}{x}\ge 0$


$\therefore x\in (0,\infty )$