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    OlympiadHardNumber Theory7–9

    Two numbers satisfy x+y=7x + y = 7 and xy=5xy = 5. What is the value of x3+y3x^3 + y^3?

    Dois números satisfazem x+y=7x + y = 7 e xy=5xy = 5. Qual é o valor de x3+y3x^3 + y^3?

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    Solution

    Step 1 of 3

    1. 1.Expanding gives (x+y)3=x3+y3+3xy(x+y)(x + y)^3 = x^3 + y^3 + 3xy(x + y).