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a^a + b^b + c^c >= 3 if a,b,c>0 with a + b + c = 3

Source: 2019 New Zealand MO Round 2 p3 NZMO

September 22, 2021
algebrainequalities

Problem Statement

Let a,ba, b and cc be positive real numbers such that a+b+c=3a + b + c = 3. Prove that aa+bb+cc≥3a^a + b^b + c^c \ge 3
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