MathDB

{(a, b, c) | ab + bc + ca> 0} when a <k (b + c), b <k (c + a) , c <k (a + b)

Source: Mathley 2014.1 p4

August 19, 2020

algebrainequalities

Problem Statement

Let

S_k

be the set of all triplets of real numbers

(a, b, c)

satisfying

a <k (b + c)

b <k (c + a)

, and

c <k (a + b)

. For what value of

k

then

S_k

is a subset of

\{(a, b, c) | ab + bc + ca> 0\}

?
Michel Bataille, France