Question

1.Aratati ca numarul este patrat perfect:2²ⁿ⁺²·4²ⁿ⁺³-2²ⁿ⁺¹·6²ⁿ⁺³

Answer 1

3²ⁿ⁺²·4²ⁿ⁺³-2²ⁿ⁺¹·6²ⁿ⁺³=3²ⁿ⁺²·2⁴ⁿ⁺⁶-2²ⁿ⁺¹·2²ⁿ⁺³·3²ⁿ⁺³=3²ⁿ⁺²·2⁴ⁿ⁺⁶-2⁴ⁿ⁺⁴·3²ⁿ⁺³=
=3²ⁿ⁺²·2⁴ⁿ⁺⁴·(2²-3)=3²ⁿ⁺²·2⁴ⁿ⁺⁴·(4-3)=3²ⁿ⁺²·2⁴ⁿ⁺⁴·1=(3ⁿ⁺¹·2²ⁿ⁺²)²