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Let a and b be the solutions to 5x^2 - 11x + 4 = 2x^2 - 7x + 9 + 7x^2 - 14x - 11. Find 1/a + 1/b.

 Dec 13, 2023
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Let a and b be the solutions to 5x^2 - 11x + 4 = 2x^2 - 7x + 9 + 7x^2 - 14x - 11. Find 1/a + 1/b.  

 

                                                         5x2 – 11x + 4  =  2x2 – 7x + 9 + 7x2 – 14x – 11   

 

Combine like terms                           5x2 – 11x + 4  =  9x2 – 21x – 2   

 

Move everything to the left side      –4x2 + 10x + 6  =  0   

 

Divide everything by –2                     2x2 – 5x – 3  =  0  

 

Factor the quadratic                          (2x + 1)(x – 3)  =  0    

 

                                                              x = –1/2  and  x = 3      These are the values of a & b.  

 

 

                                                                1           1  

                                                             ––––  +  ––––  

                                                             –1/2          3    

 

 

                                                              –2           1  

                                                             ––––  +  ––––  

                                                                1            3  

 

 

                                                              –6           1                  5  

                                                             ––––  +  ––––   =    – ––––  

                                                                3            3                  3   

.

 Dec 13, 2023

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