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((x + y)^2- 6)((x-y)^2 + 8)/(x-y)^2 >= C

Source: New Zealand NZMOC Camp Selection Problems 2013 p10

September 19, 2021
algebrainequalities

Problem Statement

Find the largest possible real number CC such that for all pairs (x,y)(x, y) of real numbers with x≠yx \ne y and xy=2xy = 2, ((x+y)2−6))(x−y)2+8))(x−y)2≥C.\frac{((x + y)^2- 6))(x-y)^2 + 8))}{(x-y)^2} \ge C. Also determine for which pairs (x,y)(x, y) equality holds.
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