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Bosnia and Herzegovina TST 1999 Day 1 Problem 1

Source: Bosnia and Herzegovina Team Selection Test 1999

September 20, 2018
algebraequationsrootsReal Roots

Problem Statement

Let aa, bb and cc be lengths of sides of triangle ABCABC. Prove that at least one of the equations x2−2bx+2ac=0x^2-2bx+2ac=0 x2−2cx+2ab=0x^2-2cx+2ab=0 x2−2ax+2bc=0x^2-2ax+2bc=0 does not have real solutions
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