3

Part of 2023 Greece JBMO TST

Problems(1)

sum (a^2 + b^2)/2ab + 2(ab + bc + ca)/3 >=5

Source: 2023 Greece JBMO TST p3/ easy version of Shortlist 2022 A6 https://artofproblemsolving.com/community/c6h3099025p28018726

a, b,

c

be positive real numbers such that

a^2 + b^2 + c^2 = 3

\frac{a^2 + b^2}{2ab} + \frac{b^2 + c^2}{2bc} + \frac{c^2 + a^2}{2ca} + \frac{2(ab + bc + ca)}{3} \ge 5

When equality holds?

algebrainequalities