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r and s are the roots of 3x^2 + 4x - 12 = 0. What is r^3 + s^3?

 Apr 30, 2022
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By Vieta

 

r +  s =   -4/3         square both sides

 

r^2 + 2rs   + s^2 =  16/9      (1)

 

And

rs =-12/3  = -4

-rs = 4

2rs  = -8                     (2)

 

Sub (2) into (1)

r^2 + s^2  - 8  =  16/9

r^2 + s^2  =  88/9

 

r^3 + s^3  =  (r + s) (r^2  - rs  + s^2) =   (-4/3) ( 88/9 + 4 ) = (-4/3) ( 124/9)=  -496  / 27

 

 

cool cool cool

 Apr 30, 2022

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