Question

If $x+\frac{1}{x}=2$, what is the value of $x^2+\frac{1}{x^2}$?

• A. $2$
• B. $4$
• C. $3$
• D. $5$

Answer 1

Answer: (A)

$2$

Given, $x+\frac{1}{x}=2$.

We need to find value of $x^2+\frac{1}{x^2}$.

We know, $(a+b{)}^2=a^2+2ab+b^2$.

On squaring both the sides, we get,

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

$\Rightarrow x^2+\frac{1}{x^2}+2\left(x\right)\left(\frac{1}{x}\right)=4$

$\Rightarrow x^2+\frac{1}{x^2}+2=4$.

Therefore, we get, $x^2+\frac{1}{x^2}=4-2=2$.