Răspuns:
a = 30
b = 12
c = 15
Explicație pas cu pas:
0,(3) = 3⁽³/9 = 1/3
0,8(3) = (83-8)/90 = 75/90⁽¹⁵ = 5/6
0,(6) = 6⁽³/9 = 2/3
a ; b ; c i.p. cu 1/3 ; 5/6 ; 2/3 =>
a/3 = b/(6/5) = c/(3/2) = k
a = 3k
b = 6k/5
c = 3k/2
a×b×c = 5400
3k×6k/5×3k/2 = 5400
54k³/10 = 5400
54k³ = 54000 | : 54
k³ = 1000
k = 10
a = 3k = 30
b = 6k/5 = 60/5 = 12
c = 3k/2 = 30/2 = 15
Verificam
30×12×15 = 5400 (adevarat ; solutiile sunt corecte)
