Question

If $x^2+\frac{1}{x^2}=51$ , find $x-\frac{1}{x}$.

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is D $7$

$x^2+\frac{1}{x^2}=51$

$x-\frac{1}{x}=?$

Apply the formula $(a-b{)}^2=a^2+b^2-2ab$

${(x-\frac{1}{x})}^2=x^2+{\left(\frac{1}{x}\right)}^2-2x\left(\frac{1}{x}\right)$

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

$=51-2=49$

$x-\frac{1}{x}=\sqrt{49}=7$