Algebra Questions

Question Number 147944 by mathdanisur last updated on 24/Jul/21

$${if}\:\:\:{x}\:+\:{y}\:+\:{z}\:=\:\mathrm{13} \\$$ $${find}\:\:\:\overline {{x},\:{yz}}\:+\:\overline {{y},\:{zx}}\:+\:\overline {{z},\:{xy}}\:=\:? \\$$

Answered by Rasheed.Sindhi last updated on 25/Jul/21

$$\:{x}+{y}+{z}=\mathrm{13}\:;\:\:\overline {{x},\:{yz}}\:+\:\overline {{y},\:{zx}}\:+\:\overline {{z},\:{xy}}=? \\$$ $$\smile\frown\smile\frown\smile\frown\smile\frown\smile\frown\smile\frown\smile\frown\smile \\$$ $$\left({x}+\frac{{y}}{\mathrm{10}}+\frac{{z}}{\mathrm{100}}\right)+\left({y}+\frac{{z}}{\mathrm{10}}+\frac{{x}}{\mathrm{100}}\right)+\left({z}+\frac{{x}}{\mathrm{10}}+\frac{{y}}{\mathrm{100}}\right) \\$$ $$=\frac{\mathrm{100}{x}+\mathrm{10}{y}+{z}}{\mathrm{100}}+\frac{\mathrm{100}{y}+\mathrm{10}{z}+{x}}{\mathrm{100}}+\frac{\mathrm{100}{z}+\mathrm{10}{x}+{y}}{\mathrm{100}} \\$$ $$=\frac{\mathrm{111}{x}+\mathrm{111}{y}+\mathrm{111}{z}}{\mathrm{100}} \\$$ $${z}=\mathrm{13}−{x}−{y}\:: \\$$ $$=\frac{\mathrm{111}{x}+\mathrm{111}{y}+\mathrm{111}\left(\mathrm{13}−{x}−{y}\right)}{\mathrm{100}} \\$$ $$=\frac{\cancel{\mathrm{111}{x}}+\cancel{\mathrm{111}{y}}+\mathrm{1443}−\cancel{\mathrm{111}{x}}−\cancel{\mathrm{111}{y}}}{\mathrm{100}} \\$$ $$=\mathrm{1443}/\mathrm{100}=\mathrm{14}.\mathrm{43} \\$$

Commented bymathdanisur last updated on 24/Jul/21

$${Thank}\:{you}\:{Ser} \\$$