Question

What is $(x+\frac{1}{x}{)}^2$?

• A. $x^2-\frac{1}{x^2}+2$
• B. $x^2+\frac{1}{x^2}-2$
• C. $x^2+\frac{1}{x^2}+2$
• D. None of the above

Answer 1

The correct option is C

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

We have the identity:
$(a+b{)}^2=a^2+b^2+2ab$
$(x+\frac{1}{x}{)}^2=x^2+{\left(\frac{1}{x}\right)}^2+2\times x\times \frac{1}{x}$
$=x^2+\frac{1}{x^2}+2$