#2**+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 !!!!

CPhill Aug 19, 2023

#3

#4**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