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AMC / AIME · Vieta's Formulas · Hard

Vieta's Formulas: If math, find math.

Roots and coefficients.

Try the problem

If α+β=αβ=3\alpha+\beta=\alpha\beta=3, find α2+β2\alpha^2+\beta^2.

Hint and answer

Concept to use

Cubics.

Hint

(α+β)2−2αβ(\alpha+\beta)^2-2\alpha\beta.

Answer

3

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