MathDB

3

Part of 2019 New Zealand MO

Problems(2)

computational from New Zealand, segments (2019 NZMO 1.3 )

Source:

1/10/2021
In triangle ABCABC, points DD and EE lie on the interior of segments ABAB and ACAC, respectively,such that AD=1AD = 1, DB=2DB = 2, BC=4BC = 4, CE=2CE = 2 and EA=3EA = 3. Let DEDE intersect BCBC at FF. Determine the length of CFCF.
geometry
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

9/22/2021
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
algebrainequalities