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a + b + d <= 3c if a^2 + ab + b^2 = 3c^2 and a^3 + a^2b + ab^2 + b^3 = 4d^3

Source: 2016 Latvia BW TST P5

December 17, 2022
algebrainequalities

Problem Statement

Given real positive numbers a,b,ca, b, c and dd, for which the equalities a2+ab+b2=3c2a^2 + ab + b^2 = 3c^2 and a3+a2b+ab2+b3=4d3a^3 + a^2b + ab^2 + b^3 = 4d^3 are fulfilled. Prove that a+b+d≤3c.a + b + d \le 3c.
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