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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.

 May 31, 2024
 #1
avatar+129487 
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Simplify as

x^2 - 6x + 13

 

uv  =  13

2uv  = 26

 

u + v =  6       square both sides

 

u^2 + 2uv + v^2  = 36

u^2 + 26 + v^2  = 36

u^2 + v^2  = 10

 

u/v^2  + v/u^2  =  [ u^3 + v^3 ] / [ uv]^2

 

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

[uv]^2 = [ 13]^2   = 169

 

 

u/v^2  + v/u^2  =  [ u^3 + v^3 ] / [ uv]^2 =  -18 / 169

 

 

cool cool cool

 May 31, 2024

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