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Let \(x\) be a positive number such that \(2x^2 = 4x + 9.\) If \(x\) can be written in simplified form as \(\dfrac{a + \sqrt{b}}{c}\) such that a, b, and c are positive integers, what is \(a + b + c\)?

 Jul 1, 2021
 #1
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Rearrange  as

 

2x^2 -  4x  -  9  =  0

 

 

x   =    4  +  sqrt  [  4^2  - 4 * 2 * - 9 ]

         _________________________

                      2 *  2

 

4  +  sqrt  [  88]

_____________

            4

 

4  +   2sqrt (22)

____________

           4

 

2   +  sqrt (22)

____________

          2

 

a = 2    b =  22     c =  2

 

Sum =    26

 

 

cool cool cool

 Jul 1, 2021
edited by CPhill  Jul 1, 2021

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