Question Number 18872 by mondodotto@gmail.com last updated on 31/Jul/17
Answered by ajfour last updated on 31/Jul/17
$$\mathrm{b}=\mathrm{a}+\frac{\mathrm{1}}{\mathrm{b}} \\ $$$$\Rightarrow\mathrm{a}=\mathrm{b}−\frac{\mathrm{1}}{\mathrm{b}}\: \\ $$
Answered by Joel577 last updated on 31/Jul/17
$${b}\:=\:{a}\:+\:\frac{\mathrm{1}}{{b}} \\ $$$${b}\:−\:\frac{\mathrm{1}}{{b}}\:=\:{a} \\ $$$${b}^{\mathrm{2}} \:−\:\mathrm{1}\:=\:{ab} \\ $$$${b}^{\mathrm{2}} \:−\:{ab}\:−\:\mathrm{1}\:=\:\mathrm{0} \\ $$