Question

Determinati numerele naturale a,b,c care verifica relatia: ab=144 bc=240 ac=60

Answer 1

$ab=a*b \\ bc=b*c \\ ac=a*c \\ a*b=144 \\ b*c=240 \\ a*c=60 \\ a*b*b*c*a*c=144*240*60 \\ a^{2}*b^{2}*c^{2}=2073600 \\ \sqrt{a^{2}*b^{2}*c^{2}}=\sqrt{2073600} \\ a*b*c=1440 \\ a=(a*b*c):(b*c)=1440:240=6 \\ b=(a*b*c):(a*c)=1440:60=24 \\ c=(a*b*c):(b*a)=1440:144=10$
In concluzie:
a=6, b=24, c=10