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Find the largest possible value of $x$ in the simplified form $x=\frac{a+b\sqrt{c}}{d}$ if $\frac{5x}{6}+1=\frac{3}{x}$, where $a,b,c,$ and $d$ are integers. What is $\frac{acd}{b}$?

 

Please help me convert this to proper latex, also, include an explanation please.

 Jul 22, 2021
edited by Guest  Jul 22, 2021
 #1
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(5/6)x  + 1  = 3/x            multiply through  by x

 

(5/6)x^2  + x  =  3           rearrange as

 

(5/6)x^2 + x  -  3   =   0 

 

Using  the   Q Formula

 

                    -1  +  sqrt  [ 1  - 4* -3 * 5/6 ]

x  =             _______________________  

                           2 (5/6)

 

x =      -1  +  sqrt  [ 11]

         _______________

                  5/3

 

              -3   + 3sqrt (11)

x  =     _______________

                       5

 

acd / b    =   (-3) (11) (5)  / 3   =     -55

 

 

cool cool cool

 Jul 22, 2021

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