Question

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

Answer 1

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

Answer 2

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