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Let u and v be the solutions to \(3x^2 + 5x + 7 = 0.\) Find \(\frac{u}{v} + \frac{v}{u}.\)
 

 Jan 24, 2021
 #1
avatar+112523 
+2

What are u and v.?     Use the quadratic formula    \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

You can do that bit yourself!

this is not a hard question.

 Jan 24, 2021
edited by Melody  Jan 24, 2021
 #2
avatar+116126 
+1

We could use the quad formula.....but....by Vieta....here's an easier  solution method.....

 

u + v =   -5/3    ⇒  (u + v)^2 = 25/9 ⇒  u^2  +  2uv  + v^2   =  25/9    ⇒   u^2 + v^2  =   25/9 - 2uv

uv = 7/3   ⇒  2uv =  2(7/3)

 

u/ v +  v/ u   =

 

(u^2 + v^2)  / uv   =

 

( 25/9  - 2uv)  / ( 7/3)   =

 

(25/9  - 2 ( 7/3)) / (7/3)  =

 

(25/9  - 14/3)  / (7/3)  =

 

(25/9 - 42/9) / (7/3)  =

 

(-17/9) ( 3/7)  =

 

(-17/7) ( 3/9)  =

 

(-17/7) (1/3)  =

 

-17/21

 

 

cool cool cool

 Jan 24, 2021
 #3
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0

Very nice! thanks!

Guest Jan 24, 2021

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