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Question Number 177152 by cortano1 last updated on 01/Oct/22

Answered by Ar Brandon last updated on 01/Oct/22

x+y=13+(√2) ...eqn(i)  y+z=20−3(√2) ...eqn(ii)  z+x=17−10(√2) ...eqn(iii)  (i)−(ii)+(iii)  ⇒2x=10−6(√2) ⇒x=5−3(√2)  ⇒y=8+4(√2) ⇒z=12−7(√2)

$${x}+{y}=\mathrm{13}+\sqrt{\mathrm{2}}\:...\mathrm{eqn}\left({i}\right) \\ $$$${y}+{z}=\mathrm{20}−\mathrm{3}\sqrt{\mathrm{2}}\:...\mathrm{eqn}\left({ii}\right) \\ $$$${z}+{x}=\mathrm{17}−\mathrm{10}\sqrt{\mathrm{2}}\:...\mathrm{eqn}\left({iii}\right) \\ $$$$\left({i}\right)−\left({ii}\right)+\left({iii}\right) \\ $$$$\Rightarrow\mathrm{2}{x}=\mathrm{10}−\mathrm{6}\sqrt{\mathrm{2}}\:\Rightarrow{x}=\mathrm{5}−\mathrm{3}\sqrt{\mathrm{2}} \\ $$$$\Rightarrow{y}=\mathrm{8}+\mathrm{4}\sqrt{\mathrm{2}}\:\Rightarrow{z}=\mathrm{12}−\mathrm{7}\sqrt{\mathrm{2}} \\ $$

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