Question

n=2016²+2016+2017 este patrat perfect




altul
n=3¹⁹-3¹⁷+3¹⁶ este patrat perfect​

Answer 1

Răspuns:

1.

$n = {2016}^{2} + 2016 + 2017 = \\ \\ = 2016 \times (2016 + 1) + 2017 = \\ \\ = 2016 \times 2017 + 2017 = \\ \\ = 2017 \times (2016 + 1) = \\ \\ = 2017 \times 2017 = \\ \\ = {2017}^{2}$

=> n este patrat perfect.

2.

$n = {3}^{19} - {3}^{17} + {3}^{16} = \\ \\ = {3}^{16} \times ( {3}^{3} - 3 + 1) = \\ \\ = {3}^{16} \times (27 - 3 + 1) = \\ \\ = {3}^{16} \times 25 = \\ \\ = {3}^{16} \times {5}^{2} = \\ \\ = ( {3}^{8} \times 5)^{2}$

=>n este patrat perfect.

Succes! ♡︎♥︎♡︎