Find the largest possible value of \(x\) in the simplified form \(x = {a \pm b\sqrt{c} \over d}\) if \(\frac{5x}{6} + 1 = \frac{3}{x}\) where \(a, b, c, \) and \(d\) are integers. What is \(\frac{acd}{b} \)?
+37146 Multipl through by x to get
5x^2 /6 + x = 3 Multiply through by 6
5x2 + 6x - 18 = 0 Quadratic Formula shows answers as ( 3 +- 3 sqrt 11 ) / 5 ..... you can finish the answer from here .....
Oops! Just realized I made a little typo. It's supposed to be \(x = {a + b\sqrt{c} \over d}\)
