Question

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

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer:

A. 2

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

$\frac{x^2+1}{x}=2$

$x^2+1=2x$

$x^2-2x+1=0$

$(x-1)^2=0$

$x-1=0$

$x=1$

$x^5+\frac{1}{x^5}$

$=1^5+\frac{1}{1^5}=1+1=2$