Question

If $x-\frac{1}{x}=2$ , then the value of $x^4+\frac{1}{x^4}$ is

• A. $4$
• B. $8$
• C. $12$
• D. $34$

Answer 1

The correct option is D $34$

$x-\frac{1}{x}=2$
squaring both side we have
${(x-\frac{1}{x})}^2=4$
$x^2+\frac{1}{x^2}-2=4$
$x^2+\frac{1}{x^2}=6$
Again squaring both side we have
$x^4+\frac{1}{x^4}-2=36$
$x^4+\frac{1}{x^4}=34$