Parte intreaga

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alex2008
Leibniz
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Parte intreaga

Post by alex2008 »

Sa se determine \( x,y,z\in \mathbb{N}^* \) astfel incat \( [\frac{x^2}{y+z}]+[\frac{y^2}{z+x}]+[\frac{z^2}{x+y}]=[\frac{2}{x+y+z}] \).
. A snake that slithers on the ground can only dream of flying through the air.
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Marius Mainea
Gauss
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Post by Marius Mainea »

Deoarece termenul din dreapta este 0, atunci fiecare parte intreaga e 0, de unde \( x^2+1\le y+z \) si analoagele.

Prin adunare \( (x-1)^2+(y-1)^2+(z-1)^2\le 0 \) si de aici \( x=y=z=1 \)
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