Solution of x+1x>2 is

x+1x>2( clearly, x≠0)⇒ x2+1x>2⇒x2+1|x|>2 ∵x2+1>0⇒ x2+1>2|x|⇒ |x|2−2|x|+1>0⇒(|x|−1)2>0⇒ |x|≠1⇒x≠−1,1∴ x∈R−{−1,0,1}

Solution of x+1x>2 is

x+1x>2( clearly, x≠0)⇒ x2+1x>2⇒x2+1|x|>2 ∵x2+1>0⇒ x2+1>2|x|⇒ |x|2−2|x|+1>0⇒(|x|−1)2>0⇒ |x|≠1⇒x≠−1,1∴ x∈R−{−1,0,1}

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

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$R - {0}$

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

$R - {1}$

$R - {- 1, 1}$

answer is B.

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Detailed Solution

$\begin{array}{l} |x + \frac{1}{x}| > 2 \\ (clearly, x \neq 0) \\ \Rightarrow |\frac{x^{2} + 1}{x}| > 2 \Rightarrow \frac{x^{2} + 1}{| x |} > 2 (∵ x^{2} + 1 > 0) \\ \Rightarrow x^{2} + 1 > 2 | x | \\ \Rightarrow | x |^{2} - 2 | x | + 1 > 0 \Rightarrow (| x | - 1)^{2} > 0 \\ \Rightarrow | x | \neq 1 \Rightarrow x \neq - 1, 1 \\ ∴ x \in R - {- 1, 0, 1} \end{array}$