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Let the roots of the equation 3x2 − 4x + 2 = 0 be alpha and beta. Find the equation with integral coefficients whose roots are (1)/(alpha3) and (1)/(beta3).

Mathematics

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Question 1 (Top Left):
The roots of the equation 3x2−4x+2=03x^2 - 4x + 2 = 0 are α\alpha and β\beta.
From Vieta's formulas:
Sum of roots: α+β=−−43=43\alpha + \beta = -\frac{-4}{3} = \frac{4}{3}
Product of roots: αβ=23\alpha \beta = \frac{2}{3}

We need to find the equation with integral coefficients whose roots are 1α3\frac{1}{\alpha^3} and 1β3\frac{1}{\beta^3}.
Let the new roots be p=1α3p = \frac{1}{\alpha^3} and q=1β3q = \frac{1}{\beta^3}.

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