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    OlympiadMediumNumber Theory7–9

    Vieta's Formulas

    Fórmulas de Vieta

    If the roots of x^{2} - 7x + 12 = 0 are r and s, find r^{2} + s^{2} without solving the equation.

    Use r + s and rs from Vieta's formulas, then (r+s)^{2} = r^{2} + 2rs + s^{2}.

    Solution

    Step 1 of 2

    1. 1.By Vieta's: r + s = 7, rs = 12.