Question

If $x+\frac{1}{x}=m,$ then find the value of $x^2+\frac{1}{x^2}:$

• A. $\frac{m^2}{4}$
• B. $m^2-2$
• C. $2m^2+1$
• D. $2m^2-1$

Answer 1

The correct option is B $m^2-2$

Given:

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

squaring both sides, we get,

${(x+\frac{1}{x})}^2=m^2$

$⟹x^2+2\times x\times \frac{1}{x}+\frac{1}{x^2}=m^2$

$⟹x^2+\frac{1}{x^2}=m^2-2$

Answer : B