If 2x + \(\frac{9}{x}\) = 9
What can be the minimum value of x2 + \(\frac{1}{x^2}\)
Answer & explanation
Correct answer: option 3
Given, 2x + \(\frac{9}{x}\) = 9
2x2 + 9 = 9x
2x2 - 9x + 9 = 0
roots are x = 3
x = \(\frac{3}{2}\)
Take, x = \(\frac{3}{2}\)
⇒ x2 + \(\frac{1}{x^2}\) = \(\frac{9}{4}\) + \(\frac{4}{9}\) = \(\frac{97}{36}\)