Question

Aflati numerele a,b,c stiind ca sunt invers proportionale cu 2,3,5 si 1supra a+ 1supra b+1 supra c=90

Answer 1

{a,b,c} i.p. {2,3,5}
$\frac{a}{ \frac{1}{2}}= \frac{b}{ \frac{1}{3}}== \frac{c}{ \frac{1}{5}}=k \\ \\ a= \frac{1} 2k;b= \frac{1}{3}k;c= \frac{1}{5}k \\ \\ \frac{1}{ \frac{1}{2}k}= \frac{1}{ \frac{1}{3}k}== \frac{1}{ \frac{1}{5}k}=90 \\ \\ \frac{2}{k} +\frac{3}{k}+ \frac{5}{k}=90 \\ \\ \frac{10}{k}=90 \\ \\ k= \frac{1}{9} \\ \\ a= \frac{1} 2* \frac{1}{9} =\frac{1}{18} \\ \\ b= \frac{1}{3}*\frac{1}{9}=\frac{1}{27} \\ \\ c= \frac{1}{5}*\frac{1}{9}=\frac{1}{45}$