If \(\sqrt {x}\) + \(\frac{1}{\sqrt {x}}\) = 3, then find the value of x2 (x2 - 47).
Answer & explanation
Correct answer: option 3
Given, \(\sqrt {x}\) + \(\frac{1}{\sqrt {x}}\) = 3
After squaring ⇒
⇒ x + \(\frac{1}{x}\) = 32 - 2 = 7
⇒ x2 + \(\frac{1}{x^2}\) = 72 - 2 = 47
Put value of 47 in ⇒ x2 (x2 - 47))
⇒ x2 (x2 - x2 - \(\frac{1}{x^2}\)) = x2 × (-) \(\frac{1}{x^2}\) = -1