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AMC / AIME · Vieta's Formulas · Medium

Vieta's Formulas: For math, find math where math are roots.

Roots and coefficients.

Try the problem

For x2−3x−1=0x^2-3x-1=0, find (α+β)2−2αβ(\alpha+\beta)^2-2\alpha\beta where α,β\alpha,\beta are roots.

Hint and answer

Concept to use

Symmetric transforms.

Hint

That expression is α2+β2\alpha^2+\beta^2.

Answer

11

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