Answer:
in steps
Explanation:
The question did not state if alpha>beta or alpha<beta, so the answer will have 2 answers for each questions
3x²-9x+2=0
x = (-(-9) ± √(-9)²-4*(3)*(2)) / (2*3)
x = (9 + √57) / 6 or x = (9 - √57) / 6 (alpha and beta) or (beta and alpha)
(I) alpha (a) ×beta (b) + alpha² × beta = ab (1+a)
= ((9 + √57) / 6) ((9 - √57) / 6) (1 + (9 ± √57))
= ((9² - (√57)²)/36) (10 ± √57)
= (24/36) (10 ± √57)
= 2/3 (10 ± √57) or (11.7 or 1.63)
(ii) alpha²-alpha×beta+beta² = a² -2ab + b² +ab = (a - b)² + ab
if a is alpha
= ((9 + √57) / 6) - ((9 - √57) / 6)) + ((9 + √57) / 6) ((9 - √57) / 6))
= √57/3 + 2/3
= (√57 + 2) / 3
if a is beta
((9 - √57) / 6) - ((9 + √57) / 6)) + ((9 - √57) / 6) ((9 + √57) / 6))
= - √57/3 + 2/3
= - (√57 + 2) / 3