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JBMO-SL 2012 A4

Solve the following equation for x,y,z∈Nx, y, z \in \mathbb{N}

(1+xy+z)2+(1+yz+x)2+(1+zx+y)2=274\left(1+\frac{x}{y+z}\right)^{2}+\left(1+\frac{y}{z+x}\right)^{2}+\left(1+\frac{z}{x+y}\right)^{2}=\frac{27}{4}

Dataset text NuminaMath olympiads. Quoted with source.

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x=y=z

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