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NMC 1992 Problem 1

  • Answer

Determine all real numbers x>1,y>1x>1, y>1, and z>1z>1, satisfying the equation

x+y+z+3x−1+3y−1+3z−1=2(x+2+y+2+z+2)\begin{aligned} x+y+z+\frac{3}{x-1} & +\frac{3}{y-1}+\frac{3}{z-1} \\ & =2(\sqrt{x+2}+\sqrt{y+2}+\sqrt{z+2}) \end{aligned}

Dataset text NuminaMath olympiads. Quoted with source.

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x=y=z=\frac{3+\sqrt{13}}{2}

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