If x2 = (\(\sqrt {2}\) -1)\(\frac{1}{2}\), then find the value of x2 + \(\frac{1}{x^2}\).
Answer & explanation
Correct answer: option 2
x2 = \(\frac{1}{\sqrt {2} - 1}\) × \(\frac{\sqrt {2} + 1}{\sqrt {2} + 1}\) = \(\sqrt {2}\) + 1
\(\frac{1}{x^2}\) = \(\sqrt {2}\) - 1
x2 + \(\frac{1}{x^2}\) = \(\sqrt {2}\) + 1 + \(\sqrt {2}\) - 1
= 2\(\sqrt {2}\)