Question

Find the value of x^2+1/x^2 if x-1/x=root 3.

Answer 1

Observe that

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

but since $\x-\frac{1}{x} = \sqrt{3}$, we can rewrite it as

$(\sqrt{3})^2 = x^2+\frac{1}{x^2}-2 \iff x^2+\frac{1}{x^2} = 3+2 = 5$

So, the answer is $5$