Question

(x , y , z ) si (2, 3,8)- invers proportionale
2x +3y -9z =420

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Answer 1

[tex]\{x,y,z\} i.p.\{2,3,8\}\Rightarrow \dfrac{x}{\frac{1}{2}}=\dfrac{y}{\frac{1}{3}}=\dfrac{z}{\frac{1}{8}}=k\Rightarrow x=\dfrac{k}{2},y=\dfrac{k}{3},z=\dfrac{k}{8}\\ 2x+3y-8z=420\\ 2\cdot \dfrac{k}{2}+3\cdot \dfrac{k}{3}-8\cdot \dfrac{k}{8}=420\\ k+k-k=420\\ \boxed{k=420}\\ x=\dfrac{k}{2}\Rightarrow \boxed{x=210}\\ y=\dfrac{k}{3}\Rightarrow \boxed{y=140}\\ z=\dfrac{k}{8}\Rightarrow \boxed{z=\dfrac{105}{2}}[/tex]