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1 +1/x + 2(x + 1)/xy + 3(x + 1)(y + 2)/xyz+4(x + 1)(y + 2)(z + 3)/xyz=0

Source: 2019 Irish Mathematical Olympiad paper 1 p4

October 5, 2020
algebraequation

Problem Statement

Find the set of all quadruplets (x,y,z,w)(x,y, z,w) of non-zero real numbers which satisfy 1+1x+2(x+1)xy+3(x+1)(y+2)xyz+4(x+1)(y+2)(z+3)xyzw=01 +\frac{1}{x}+\frac{2(x + 1)}{xy}+\frac{3(x + 1)(y + 2)}{xyz}+\frac{4(x + 1)(y + 2)(z + 3)}{xyzw}= 0
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