Question

Determinati numerele a,b si c invers proportionale cu numerele 2,3 si 7 stiind ca a-b-c=1.

Answer 1

{a,b,c} i.p. {2,3,7} =>$\frac{a}{ \frac{1}{2} }= \frac{b}{ \frac{1}{3} } = \frac{c}{ \frac{1}{7} }=k=>a= \frac{1}{2}k \\ b= \frac{1}{3}k \\ c= \frac{1}{7}k \\ => \frac{1}{2}k- \frac{1}{3} k- \frac{1}{7}k=1=> \frac{21}{42}k - \frac{14}{42} k- \frac{6}{42}k=1=> \frac{1}{42}k=1=> \\ k= 42=>a=21 \\ b=14 \\ c=6$