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

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

 Mar 10, 2024
 #1
avatar+129743 
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First one

3x^2 - 18x + 13 =  0

ab  = 13/3

a + b =  18/3 =  6

1/a  + 1/b =   (a + b)  / (ab)  =  6 / (13/3)  =  18 / 13

 

Second one

4x^2 + x + 11  = 0

uv = 11/4

u + v = - 1/4     square both sides

u^2 + 2(uv) + v^2  = 1/16

u^2 + 2(11/4) + v^2  = 1/16

u^2 + v^2   = 1/16 - 22/4

u^2 + v^2  = -87 / 16

 

u / v  +  v /u   = 

 

[ u^2 + v^2  ]  / [ uv ]  =    (-87/16) /( 11/4) =   (-87/16)(4/11)  = -87/44

 

 

cool cool cool

 Mar 10, 2024

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