+0  
 
0
39
4
avatar

Let u and v be the solutions to 3x^2 + 5x + 7 = 2x^2 - 4x - 11. Find u/v + v/u.

 Oct 19, 2022
 #2
avatar
0

 

Let u and v be the solutions to 3x^2 + 5x + 7 = 2x^2 - 4x - 11. Find u/v + v/u.  

 

 

Start with the given                                                   3x2 + 5x + 7  =  2x2 - 4x - 11 

 

Subtract 2x2 – 4x – 11 from both sides to obtain       x2 + 9x +18  =  0  

 

Factor that resultant equation                                  (x + 6)(x + 3)  =  0  

 

Therefore the two solutions to the quadratic are       x = –6  and  x = –3  

 

So one of them is "u" and the other is "v"  

 

We want the solution to                                               (–6 / –3) + (–3 / –6)   

 

What this equals is                                                       (2) + (1/2)  

 

So the answer is                                                           5/2  or  2.5  

.

 Oct 20, 2022

31 Online Users