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avatar+82 

Let $r$ and $s$ be the roots of $3x^2 + 4x - 12 = 0.$ Find $r^2 + s^2.$

 Aug 19, 2023
 #2
avatar+126966 
+1

By Vieta

The sum of the   roots  =  -4 / 3

So

r + s = -4/3          square both sides

 

r^2  + 2rs + s^2  =  16/9

 

And the product of the  roots   = -12/ 3 =  -4  = rs

So

2rs = 2 (-4) =  -8

 

So

 

r^2 + 2rs + s^2 = 16/9

 

r^2 - 8 + s^2  = 16/9

 

r^2 + s^2  =  16/9 + 8  =  88/9

 

CORRECTED  !!!!....thx to The 3Mathketeers for  catching  my error  !!!!

 

 

cool cool cool

 Aug 19, 2023
edited by CPhill  Aug 30, 2023
edited by CPhill  Aug 30, 2023
 #3
avatar+82 
0

Thanks for trying but those arent' the correct answers

 Aug 19, 2023
 #4
avatar+177 
0

I am quite impressed with Cphill's procedure! Unfortunately, Cphill made a mistake when he subtracted 8 from both sides instead of adding 8 to both sides! If you correct that mistake, you should get the right answer!

 

Unfortunately, this answer is not posting because the AI moderation is not posting it. I will add some filler text because that makes the AI believe that I am writing a complete answer. You, as a reader, need not read further that this sentence.

 

If I add more filler text, then it is more likely that the AI language model will actually post my answer. At least, that is what I think? I hope I am right because I am just trying to point out an error that I found in one of the most recent answers.

The3Mathketeers  Aug 20, 2023
edited by The3Mathketeers  Aug 20, 2023
edited by The3Mathketeers  Aug 20, 2023

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