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For-0-x-y-z-1-solve-the-equation-x-1-y-zx-y-1-z-xy-z-1-x-yz-3-x-y-z-




Question Number 4752 by Yozzii last updated on 04/Mar/16
For 0≤x,y,z≤1 solve the equation  (x/(1+y+zx))+(y/(1+z+xy))+(z/(1+x+yz))=(3/(x+y+z)).
$${For}\:\mathrm{0}\leqslant{x},{y},{z}\leqslant\mathrm{1}\:{solve}\:{the}\:{equation} \\ $$$$\frac{{x}}{\mathrm{1}+{y}+{zx}}+\frac{{y}}{\mathrm{1}+{z}+{xy}}+\frac{{z}}{\mathrm{1}+{x}+{yz}}=\frac{\mathrm{3}}{{x}+{y}+{z}}. \\ $$
Commented by prakash jain last updated on 05/Mar/16
trivial solution is x=y=z=1  Other solution to be worked.
$$\mathrm{trivial}\:\mathrm{solution}\:\mathrm{is}\:{x}={y}={z}=\mathrm{1} \\ $$$$\mathrm{Other}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{be}\:\mathrm{worked}. \\ $$

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