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ad + bc = x, ac + bd = y, ab + cd = z, one of a, b,c,d equals to sum of other 3

Source: Czech-Polish-Slovak Junior Match 2018, individual p1 CPSJ

February 1, 2020
Sumsystem of equationsalgebra

Problem Statement

Are there four real numbers a,b,c,da, b, c, d for every three positive real numbers x,y,zx, y, z with the property ad+bc=xad + bc = x, ac+bd=yac + bd = y, ab+cd=zab + cd = z and one of the numbers a,b,c,da, b, c, d is equal to the sum of the other three?
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