Question

Produsul a trei numere consecutive este cu 48 mai mare decat produsuln primelor doua. Determinati cele trei numere naturale.

Answer 1

$a \cdot(a+1)\cdot(a+2)=48+a\cdot(a+1) \\ \\ a \cdot(a+1)\cdot(a+2)-a\cdot(a+1)=48 \\ \\ a(a+1)(a+2-1) = 48 \\ \\ a(a+1)(a+1) = 48 \\ \\ a(a+1)^2 = 48 \\ \\ \rightarrow \boxed{a=\boxed{3}} \\ \\ \boxed {a+1 = 3+1 =\boxed{ 4}} \\ \\ \boxed {a+2 = 3+2 = \boxed{5}}$

Answer 2

a(a+1)(a+2) = 48 + a(a+1) => a(a+1)(a+2) - a(a+1) = 48 <=>

a(a+1)(a+2-1) = 48 => a(a+1)(a+1) =48

48 = 3 x 4 x 4 => a = 3 ; a+1 = 4 ; a+2 = 5