Question

Sa se determine numerele x,y,z direct proportionele cu numerele 3,5 si 6 stiind ca 2x-3y+2z=6

Answer 1

$\frac{x}{3}= \frac{y}{5}= \frac{z}{6}=k \Rightarrow x=3k,~y=5k~si~z=6k. \\ \\ 2x-3y+2z=6 \Leftrightarrow 2 \cdot 3k-3 \cdot 5k+2 \cdot 6k=6 \Leftrightarrow 6k-15k+12k=6 \Leftrightarrow \\ \\ \Leftrightarrow 3k=6 \Rightarrow k=2.\\ \\ Deci~x=3k=3 \cdot 2=6; ~~y=5k=5 \cdot 2=10~~~si~~~z=6k=6 \cdot 2=12. \\ \\ \\ \\ .$