Question

Fie a, b, si c trei numere naturale astfel incat a/b =7/15 si b/c= 3/8
a) verificaţi egalitatea (a+b) la puterea a doua= ala a doua + 2ab+ b la a doua
b) aratati ca c= 5 (b-a)
c) Determinaţi numerele a, b, si c dacă a+b+c=124

Answer 1

a/b = 7/15     a = 7b/15
b/c = 3/8        c = 8b/3
a)     (a+b)² = (7b/15 + b)² = (22b/15)² = 484b²/225
a² + 2ab + b² = 49b² /225 + 14b² /15 + b² = 484b² /225 ⇒
⇒  (a+b)² = a² + 2ab + b²
b) b - a = b - 7b/15 = 8b/15
5(b-a) = 8b/3 = c
c)  a+b+c = 124
7b/15 + b +8b/3 = 62b/15 = 124     b/15 = 2    b = 30    a = 14    c = 80