Question

The number of real roots of the equation ${(x+\frac{1}{x})}^3+(x+\frac{1}{x})=0$, is

• A. $2$
• B. $0$
• C. $3$
• D. $1$

Answer 1

The correct option is B $0$

${(x+\frac{1}{x})}^3+(x+\frac{1}{x})=0$
$\Rightarrow (x+\frac{1}{x})[{(x+\frac{1}{x})}^2+1]$
Since, ${(x+\frac{1}{x})}^2+1>0$
Therefore, $(x+\frac{1}{x})=0$
$\Rightarrow x^2+1=0$
Therefore, number of real roots are zero.
Ans: B