If x2 - \(\sqrt[2]{10}\)x + 1 = 0, then find x - \(\frac{1}{x}\)
Answer & explanation
Correct answer: option 1
Formula → [If x + \(\frac{1}{x}\) = M, x - \(\frac{1}{x}\) = \(\sqrt {M^2 - 4}\)]
x2 - \(\sqrt[2]{10}\)x + 1 = 0
x2 + 1 = \(\sqrt[2]{10}\)x
x + \(\frac{1}{x}\) = \(\sqrt[2]{10}\)
x - \(\frac{1}{x}\) = \(\sqrt {(\sqrt[2]{10})^2 - 4}\)
x - \(\frac{1}{x}\) = \(\sqrt {6}\)