Question

If $m-\frac{1}{m}=5$, then find $m^2+\frac{1}{m^2}$

• A. 25
• B. 30
• C. 22
• D. 27

Answer 1

The correct option is D 27

Applying the formula, ${(a-b)}^2=a^2+b^2-2ab$
${(m-\frac{1}{m})}^2=m^2+{\left(\frac{1}{m}\right)}^2-2m\times \frac{1}{m}=m^2+\frac{1}{m^2}-2$
$=>m^2+\frac{1}{m^2}={(m-\frac{1}{m})}^2+2$
Substituting $m-\frac{1}{m}=5$,
$=>m^2+\frac{1}{m^2}=5^2+2=25+2=27$