3

Part of 2009 Dutch IMO TST

Problems(1)

in R+: a + b + c >= abc =>a^2 + b^2 + c^2 >= \sqrt3 abc

Source: 2009 Dutch IMO TST P3

a, b

c

be positive reals such that a + b + c \ge abc. Prove that a^2 + b^2 + c^2 \ge \sqrt3 abc.

inequalities3-variable inequalitythree variable inequality