If x8 + 1 - 34x4 = 0, x > 0, then
find (\(\frac{x^6 + \frac{1}{x^6}}{2}\))
Answer & explanation
Correct answer: option 3
Given, x8 + 1 - 34x4 = 0
taking x4 common, then
⇒ x4 + \(\frac{1}{x^4}\) = 34
⇒ x2 + \(\frac{1}{x^2}\) = \(\sqrt {34 + 2}\) = 6
⇒ x6 + \(\frac{1}{x^6}\) = (6)3 - 3 × 6 = 198
So, (\(\frac{x^6 + \frac{1}{x^6}}{2}\)) = \(\frac{198}{2}\) = 99