Question

pls imi trebuie maine​

Answer 1

Explicație pas cu pas:

$A = 2^{n+1} \cdot 5^{n+1} + 3 \cdot 2^{n} \cdot 5^{n+1} - 2^{n+3} \cdot 5^{n} = 2 \cdot 2^{n} \cdot 5 \cdot 5^{n} + 3 \cdot 2^{n} \cdot 5 \cdot 5^{n} - {2}^{3} \cdot 2^{n} \cdot 5^{n} = 2^{n} \cdot 5^{n} \cdot (10 + 15 - 8) = 2^{n} \cdot 5^{n} \cdot 17 \ \ \red{ \bf \vdots \ \ 17}$

A are exact 50 de divizori naturali:

$(n + 1)(n+1)(1 + 1) = 50 \\ 2(n + 1)^{2} = 50 \iff (n + 1)^{2} = 25$

$(n + 1)^{2} = 5^{2} \iff n + 1 = 5 \\ \implies \bf n = 4$