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max (a^2/b,b^2/a) max (c^2/d,d^2/c) =(min (a + b, c + d))^4

Source: Dutch IMO TST2 2019 p2

January 11, 2020
algebrasystem of equationsmax and minmaxmin

Problem Statement

Determine all 44-tuples (a,b,c,d)(a,b, c, d) of positive real numbers satisfying a+b+c+d=1a + b +c + d = 1 and max⁡(a2b,b2a)⋅max⁡(c2d,d2c)=(min⁡(a+b,c+d))4\max (\frac{a^2}{b},\frac{b^2}{a}) \cdot \max (\frac{c^2}{d},\frac{d^2}{c}) = (\min (a + b, c + d))^4
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