Question Number 18779 by chux last updated on 29/Jul/17
$$\mathrm{If}\:\:\frac{\mathrm{1}}{\mathrm{2x}}+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2x}}+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2x}}+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2x}}+......=\mathrm{y}\right.\right.\right. \\ $$$$\mathrm{what}\:\mathrm{does}\:\mathrm{x}\:\mathrm{equals}? \\ $$$$ \\ $$$$\left.\mathrm{a}\right)\mathrm{1}/\mathrm{2} \\ $$$$\left.\mathrm{b}\right)\mathrm{2}/\mathrm{4} \\ $$$$\left.\mathrm{c}\right)\mathrm{1} \\ $$$$\left.\mathrm{d}\right)\mathrm{1}/\mathrm{4} \\ $$
Commented by chux last updated on 29/Jul/17
$$\mathrm{i}\:\mathrm{noticed}\:\mathrm{that}\:\mathrm{too}\:\mathrm{when}\:\mathrm{i}\:\mathrm{tried} \\ $$$$\mathrm{to}\:\mathrm{solve}\:\mathrm{it}.\mathrm{I}\:\mathrm{was}\:\mathrm{astonished}\:\mathrm{when}\:\mathrm{i}\: \\ $$$$\mathrm{discovered}\:\mathrm{that}\:\mathrm{it}\:\mathrm{had}\:\mathrm{options}\: \\ $$$$\mathrm{which}\:\mathrm{are}\:\mathrm{fractions}\:\mathrm{of}\:\mathrm{numbers}. \\ $$
Commented by dioph last updated on 29/Jul/17
$${y}\:=\:\frac{\mathrm{1}}{\mathrm{2}{x}}\:+\:\frac{\mathrm{1}}{\mathrm{2}}{y} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{y}\:=\:\frac{\mathrm{1}}{\mathrm{2}{x}} \\ $$$${x}\:=\:\frac{\mathrm{1}}{{y}},\:\forall{y}\:\neq\:\mathrm{0} \\ $$