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Let u and v be the solutions to 3x^2 + 5x + 7 = 2x^2 + 11x - 6.  Find u/v^2 + v/u^2.

 Mar 26, 2024
 #1
avatar+128794 
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x^2  - 6x + 13  =  0

 

uv = 13

(uv)^2  = u^2v^2  = 169

 

u + v =  6    square both sides

u^2 + 2uv + v^2   = 36

u^2 + 2(13) + v^2  = 36

u^2 + v^2  =  10

 

u^3  + v^3 = ( u + v) ( u^2 + v^2  - uv) =   (6) ( 10 - 13) =  -18

 

u / v^2  + v / u^2  = 

 

[ u^3 + v^3 ] / [ u^2v^2 ]  =

 

-18  / 169

 

cool cool cool

 Mar 27, 2024

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