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    OlympiadMediumAlgebra7–9

    Two numbers satisfy a−b=3a - b = 3 and ab=10ab = 10. What is the value of a2+b2a^{2} + b^{2}?

    Dois números satisfazem a−b=3a - b = 3 e ab=10ab = 10. Qual é o valor de a2+b2a^{2} + b^{2}?

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    Solution

    Step 1 of 3

    1. 1.Square the difference: (a−b)2=a2−2ab+b2(a - b)^{2} = a^{2} - 2ab + b^{2}, so a2+b2=(a−b)2+2aba^{2} + b^{2} = (a - b)^{2} + 2ab.