The roots of the equaion 3x^2-8x+2=0 are alfa and beta. Find the values of alfa/beta + beta/alfa and alfa^4 + beta^4. with explanation if can pls. thannks in advance.
Originally posted by weakinmath:The roots of the equaion 3x^2-8x+2=0 are alfa and beta. Find the values of alfa/beta + beta/alfa and alfa^4 + beta^4. with explanation if can pls. thannks in advance.
Lazy to figure out the shortcut, so let us take the longcut.
3x^2 - 8x + 2 = 0
Using quadratic formula, x = (4 + sqrt(10)) / 3 or x = (4 - sqrt(10)) / 3
(alpha/beta) + (beta/alpha) + alpha^4 + beta^4
= [[(4 + sqrt(10)) / 3] / [(4 - sqrt(10)) / 3]] + [[(4 - sqrt(10)) / 3] / [(4 + sqrt(10)) / 3]] + [(4 + sqrt(10)) / 3]^4 + [(4 - sqrt(10)) / 3]^4
= 3334/81
This method may seem useless and longwinded, but in exam, if you are in panic mode like I was a few times in the past, doing this will actually save you some marks, even if you are unable to finish the entire thing.