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3ab < 1 if ax^2 +b=x+1/x has ezctly 2 roots

Source: 2014 Cuba 2.8

September 20, 2024
algebrainequalities

Problem Statement

Let aa and bb be real numbers. It is known that the graph of the parabola y=ax2+by =ax^2 +b cuts the graph of the curve y=x+1/xy = x+1/x in exactly three points. Prove that 3ab<13ab < 1.
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