Question

NR.2,3,4,SUNT INVERS PROPORTIONALE CU A, B, C SI A X B X C =1\3 CALCULATI A, B, C.

Answer 1

[tex]\{2,3,4\}i.p.\{a,b,c\}=\ \textgreater \ \frac{2}{\frac{1}{a}}=\frac{3}{\frac{1}{b}}=\frac{4}{\frac{1}{c}}=k=\ \textgreater \ \\ 2=\frac{k}{a}=\ \textgreater \ a=\frac{k}{2}\\ 3=\frac{k}{b}=\ \textgreater \ b=\frac{k}{3}\\ 4=\frac{k}{c}=\ \textgreater \ c=\frac{k}{4}\\ a*b*c=\frac{1}{3}\\ \frac{k}{2}*\frac{k}{3}*\frac{k}{4}=\frac{1}{3}\\ \frac{k^3}{24}=\frac{1}{3}\\ k^3=8=\ \textgreater \ k=2\\ a=1,b=\frac{3}{2},c=\frac{1}{2}[/tex]