Question Number 177152 by cortano1 last updated on 01/Oct/22
Answered by Ar Brandon last updated on 01/Oct/22
$${x}+{y}=\mathrm{13}+\sqrt{\mathrm{2}}\:...\mathrm{eqn}\left({i}\right) \\ $$$${y}+{z}=\mathrm{20}−\mathrm{3}\sqrt{\mathrm{2}}\:...\mathrm{eqn}\left({ii}\right) \\ $$$${z}+{x}=\mathrm{17}−\mathrm{10}\sqrt{\mathrm{2}}\:...\mathrm{eqn}\left({iii}\right) \\ $$$$\left({i}\right)−\left({ii}\right)+\left({iii}\right) \\ $$$$\Rightarrow\mathrm{2}{x}=\mathrm{10}−\mathrm{6}\sqrt{\mathrm{2}}\:\Rightarrow{x}=\mathrm{5}−\mathrm{3}\sqrt{\mathrm{2}} \\ $$$$\Rightarrow{y}=\mathrm{8}+\mathrm{4}\sqrt{\mathrm{2}}\:\Rightarrow{z}=\mathrm{12}−\mathrm{7}\sqrt{\mathrm{2}} \\ $$