Question

13.Aratati ca numarul x este patrat perfect, pentru orice numar n=N, unde x=…

Answer 1

Răspuns:

x= 3²ⁿ⁺³•4²ⁿ⁺³-2²ⁿ⁺¹•6²ⁿ⁺³

x=3²ⁿ·3³·2⁴ⁿ·2⁶-2²ⁿ·2·2²ⁿ·2³·3²ⁿ·3³

x=3²ⁿ⁺³·2⁴ⁿ⁺⁶- 3²ⁿ⁺³·2⁴ⁿ⁺⁴

x=3²ⁿ⁺²·2⁴ⁿ⁺⁴(3·4-3)

x=(3ⁿ⁺¹·2²ⁿ⁺²)²·9

x=(3ⁿ⁺¹·2²ⁿ⁺²·3)²

x=(3ⁿ⁺²·2²ⁿ⁺²)² => patrat perfect