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Question Number 151481 by mathdanisur last updated on 21/Aug/21

if  x;y;z;t∈R  and  x+y+z ≤ 3t  ;  y+z+t ≤ 3x  z+t+x ≤ 3y  ;  t+x+y ≤ 3z  compare:  x;y;z;t

$$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z};\mathrm{t}\in\mathbb{R}\:\:\mathrm{and} \\ $$$$\mathrm{x}+\mathrm{y}+\mathrm{z}\:\leqslant\:\mathrm{3t}\:\:;\:\:\mathrm{y}+\mathrm{z}+\mathrm{t}\:\leqslant\:\mathrm{3x} \\ $$$$\mathrm{z}+\mathrm{t}+\mathrm{x}\:\leqslant\:\mathrm{3y}\:\:;\:\:\mathrm{t}+\mathrm{x}+\mathrm{y}\:\leqslant\:\mathrm{3z} \\ $$$$\mathrm{compare}:\:\:\mathrm{x};\mathrm{y};\mathrm{z};\mathrm{t} \\ $$

Commented by dumitrel last updated on 21/Aug/21

x=y=z=t

$${x}={y}={z}={t} \\ $$

Commented by mathdanisur last updated on 21/Aug/21

Thank You Dear Ser  Solution please

$$\mathrm{Thank}\:\mathrm{You}\:\mathrm{Dear}\:\boldsymbol{\mathrm{S}}\mathrm{er} \\ $$$$\mathrm{Solution}\:\mathrm{please} \\ $$

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