in R+: a + b + c >= abc =>a^2 + b^2 + c^2 >= \sqrt3 abc
Source: 2009 Dutch IMO TST P3
January 10, 2020
inequalities3-variable inequalitythree variable inequality
Problem Statement
Let and be positive reals such that a + b + c \ge abc. Prove that a^2 + b^2 + c^2 \ge \sqrt3 abc.