+82 Let $r$ and $s$ be the roots of $3x^2 + 4x - 12 = 0.$ Find $r^2 + s^2.$
+128732 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 !!!!
+177 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.
