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Question Number 58622 by mr W last updated on 26/Apr/19

$$solve$$$$x+y=2xy$$$$y+z=3yz$$$$z+x=7zx$$

Commented by rahul 19 last updated on 26/Apr/19

$$x=y=z=0.$$

Commented by mr W last updated on 26/Apr/19

$$thanks!$$

Answered by tanmay last updated on 26/Apr/19

$$\frac{1}{y}+\frac{1}{x}=2$$$$\frac{1}{z}+\frac{1}{y}=3$$$$\frac{1}{x}+\frac{1}{z}=7$$$$2(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})=12$$$$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=6$$$$\frac{1}{x}=6-3=3\to x=\frac{1}{3}$$$$\frac{1}{y}=6-7=-1\to y=-1$$$$\frac{1}{z}=6-2=4\to z=\frac{1}{4}$$

Commented by mr W last updated on 26/Apr/19

$$nicesolutionsir,thanks!$$

Commented by tanmay last updated on 27/Apr/19

$$mostwelcomesir...$$

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