MathDB

Equal signs needed

Source: Kyiv City MO 2023 9.2

May 14, 2023

algebra

Problem Statement

Non-zero real numbers

a, b

and

c

are given such that

ab+bc+ac=0

. Prove that numbers

a+b+c

and

\dfrac{1}{a+b}+\dfrac{1}{b+c}+\dfrac{1}{a+c}

are either both positive or both negative. Proposed by Mykhailo Shtandenko