Question

DAU COROANA SI 20 DE PUNCTE!
Calculati numerele naturale a, b si c invers proportionale cu numerele 2, 3,5 si 2,(3) stiind ca A*B*C=36288

Answer 1

$2a=3,5b=2,(3)c=k=\ \textgreater \ a= \frac{k}{2};~b= \frac{k}{3,5}= \frac{k}{ \frac{7}{2} } = \frac{2k}{7}~si \\ c= \frac{k}{2,(3)}= \frac{k}{ \frac{23-2}{9} }= \frac{k}{ \frac{21}{9} } = \frac{9k}{21}= \frac{3k}{7} . \\ \\ a*b*c=36288\ \textless \ =\ \textgreater \ \frac{k}{2}* \frac{2k}{7}* \frac{3k}{7} =36288\ \textless \ =\ \textgreater \ \frac{3 k^{3} }{49} =36288=\ \textgreater \ \\ =\ \textgreater \ k ^{3} = \frac{49*36288}{3}= 592704=\ \textgreater \ \boxed{k=84}. \\ \\ a= \frac{k}{2}= \frac{84}{2}=42. \\ b= \frac{2k}{7}= \frac{2*84}{7}=24. \\ c= \frac{3k}{7}= \frac{3*84}{7}= 36.$