Răspuns:
a = 56 ; b = 84 ; c = 126
Explicație pas cu pas:
a/8 = b/12 = c/18 =>
a = 8b/12 = 2b/3
c = 18b/12 = 3b/2
a•b•c = 84³
2b/3 • b • 3b/2 = 84³ =>
b³ = 84³ => b = 84 =>
a = 2•84:3 => a = 56
c = 3•84:2 => c = 126
84 = 7•2²•3 ; 56 = 7•2³ ; 126 = 7·3²·2
a•b•c = 56•84•126 = 7•2³•7•2²•3•7•3²•2 =
=7³•2⁶•3³= (7•2²•3)³ = 84³
