Question

Solution of $|x+\frac{1}{x}|>2$ is

• A. $R-\left\{0\right\}$
• B. $R-\{-1,0,1\}$
• C. $R-\left\{1\right\}$
• D. $R-\{-1,1\}$

Answer 1

Answer: (B)

$R-\{-1,0,1\}$

$|x+\frac{1}{x}|2$

But $\frac{1}{x}\to \infty$ if $x=0$

$\therefore x\ne 0$

if $x>0$

$x+\frac{1}{x}>2$ only if $x\ne 1$

if $x<0$

$x+\frac{1}{x}<-2$ only if $x\ne -1$

Solution: $R-\{-1,0,1\}$