Question

If $(x^2+\frac{1}{x^2})=66$, then $(x-\frac{1}{x})$ is equal to

• A. 6
• B. 12
• C. 8
• D. 9

Answer 1

Answer: (C)

8

${(x-\frac{1}{x})}^2=x^2+\frac{1}{x^2}-2\times x\times \frac{1}{x}$
$=x^2+\frac{1}{x^2}-2$
${(x-\frac{1}{x})}^2=66-2=64$
$\Rightarrow (x-\frac{1}{x})=8$
Option C is correct.