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Russian algebra with two polynomials

Source: Caucasus MO 2023, day 1, senior P2

March 10, 2023
algebrapolynomial

Problem Statement

Given are reals a,ba, b. Prove that at least one of the equations x4−2b3x+a4=0x^4-2b^3x+a^4=0 and x4−2a3x+b4=0x^4-2a^3x+b^4=0 has a real root.
Proposed by N. Agakhanov
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