Step-by-step explanation:
α and β are roots of 3x² - 6x + 5 = 0.
By Vieta's Formula,
we have αβ = 5/3 and α + β = 2.
To find the equation with roots α + β and 2/(α + β),
we find the Sum and Product of these roots.
=> Sum = (α + β) + 2/(α + β) = (2) + 2/(2) = 3.
=> Product = (α + β) * 2/(α + β) = 2.
Hence we have Ax² + Bx + C,
where -B/A = 3 and C/A = 2.
Simplest form is A = 1, B = -3, and C = 2.
Hence the equation with roots
α + β and 2/(α + β) is x² - 3x + 2.
