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2019 Junior Balkan MO, Problem 2

Source: 2019 Junior Balkan MO

June 22, 2019
algebraJuniorJBMO2019Balkaninequalities

Problem Statement

Let aa, bb be two distinct real numbers and let cc be a positive real numbers such that
a4−2019a=b4−2019b=ca^4 - 2019a = b^4 - 2019b = c.
Prove that −c<ab<0- \sqrt{c} < ab < 0.
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