Răspuns:
Explicație pas cu pas:
Fie a, b si c cele trei numere
[a; b; c] i.p. [ 2; 3; 4]
=> a/(1/2) = b/ ( 1/3) = c/(1/4) = k
=> a : ( 1/2) = k => 2 a = k
=> 2 a = 3 b = 4 c = k
=> a = k/2; b = k/3 si c = k/4
_________________________
a × b × c = 72
k/2 × ( k/3) × (k/4) = 72
k³/(2×3×4) = 72
k³/24 = 72
k³ = 24×72
k³ = 3³×2³×2³
k = ∛(3×2×2)³
k = 3×4
k = 12
___________________
a = k/2 = 12/2 => a = 6
b = k/3 = 12/3 => b = 4
c = k/4 = 12/4 => c = 3
Verific:
a × b × c = 6 × 4 × 3 = 72 → produsul numerelor
