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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 \(\frac{acd}{b} \)

 Oct 16, 2020
 #1
avatar+27725 
+1

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 .....

 
 Oct 16, 2020
 #2
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Oops! Just realized I made a little typo. It's supposed to be \(x = {a + b\sqrt{c} \over d}\)

 
 Oct 16, 2020
 #3
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Thanks ElectricPavlov! You were correct, and now I understand! smiley

 
 Oct 16, 2020
 #4
avatar+27725 
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You're welcome !  cheeky

 
ElectricPavlov  Oct 16, 2020

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