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Let u and v be the solutions to 3x^2 + 5x + 7 = 2x^2 + 5x - 19.  Find \frac{u}{v} + \frac{v}{u}.

 Dec 14, 2023
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Let u and v be the solutions to 3x^2 + 5x + 7 = 2x^2 + 5x - 19.  Find \frac{u}{v} + \frac{v}{u}. 

 

 

                                                 3x2 + 5x + 7  =  2x2 + 5x – 19  

 

Combine like terms                     x2  =  –26  

 

therefore                                     x  =  + sqrt(–26)

 

                                                   Call u  =  + sqrt(–26)  

                                                   Call v  =  – sqrt(–26) 

 

 

 u       + sqrt(–26)                               v       – sqrt(–26)  

––  =  ––––––––––  =  –1                 ––  =  ––––––––––  =  –1  

 v        – sqrt(–26)                              u        + sqrt(–26)  

 

therefore                                       u/v + v/u  =  –1 + (–1)  

 

                                                      u/v + v/u  =  –2   

.

 Dec 14, 2023

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