Question

If $x+\frac{1}{x}=2then(x^5+\frac{1}{x^5})$ is

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is A $2$

$x+\frac{1}{x}=2$
On squaring eq. (1). we get
$\Rightarrow x^2+\frac{1}{x^2}+2.x\frac{1}{x}=4\Rightarrow x^2+\frac{1}{x^2}=2$
On cubing eq. (1). we get
And $x^3+\frac{1}{x^3}+3.x\times \frac{1}{x}(x+\frac{1}{x})=8$
$\Rightarrow x^3+\frac{1}{x^3}=2$
$(x^2+\frac{1}{x^2})\times (x^3+\frac{1}{x^3})=x^5+\frac{1}{x}+x+\frac{1}{x^5}$
$\Rightarrow x^5+\frac{1}{x^5}=2\times$ $2-2$
$\Rightarrow x^5+\frac{1}{x^5}$ = $2$