Question

Aratati ca numarul 3⁷² + 2•3⁷³+3⁷⁴ este oatrat perfect?
repede va rog​

Answer 1

Explicație pas cu pas:

$\bf\red\:3 {}^{72} + 2 \times 3 {}^{73} + 3 {}^{74} \\ \bf\red\:= 3 {}^{72} + 2 \times 3 {}^{1 + 72} + 3 {}^{2 + 72} \\ \bf\red\:= 3 {}^{72} + 2 \times 3 \times 3 {}^{72} + 3 {}^{2} \times 3 {}^{72} \\ \bf\red\: = 3 {}^{72} \times (1 + 2 \times 3 + 3 {}^{2} ) \\ \bf\red\: = 3 {}^{72} \times (1 + 6 + 9) \\ = \bf\red\:3 {}^{72} \times 16 \\ \bf\red\: = (3 {}^{36} ) {}^{2} \times 4 {}^{2} \\ \bf\red\:= (3 {}^{36} \times 4) {}^{2} → patrat \: perfect$