Răspuns: [tex]\color{Crimson}\large \boxed{\bf A = (2^{2n}\cdot 10)^{2}\longrightarrow patrat~perfect}[/tex]
Explicație pas cu pas:
[tex]\large \bf A = 8^{n+1}\cdot 2^{n+3} + 3 \cdot 8^{n} \cdot 2^{n+1}+ 15 \cdot 8^{n}\cdot 2^{n+1}[/tex]
[tex]\large \bf A = (2^{3} )^{n+1}\cdot 2^{n+3} + 3 \cdot (2^{3} )^{n} \cdot 2^{n+1}+ 15 \cdot (2^{3} )^{n}\cdot 2^{n+1}[/tex]
[tex]\large \bf A = 2^{3n+3}\cdot 2^{n+3} + 3 \cdot 2^{3n} \cdot 2^{n+1}+ 15 \cdot 2^{3n}\cdot 2^{n+1}[/tex]
[tex]\large \bf A = 2^{3n+3+n+3}+ 3 \cdot 2^{3n+n+1} + 15 \cdot 2^{3n+n+1}[/tex]
[tex]\large \bf A = 2^{4n+6}+ 3 \cdot 2^{4n+1} + 15 \cdot 2^{4n+1}[/tex]
[tex]\large \bf A = 2^{4n}\cdot (2^{6}+ 3 \cdot 2^{1} + 15 \cdot 2^{1})[/tex]
[tex]\large \bf A = 2^{4n}\cdot (64+ 6 + 15 \cdot 2)[/tex]
[tex]\large \bf A = 2^{4n}\cdot (64+ 6 + 30)[/tex]
[tex]\large \bf A = 2^{4n}\cdot 100[/tex]
[tex]\large \bf A = 2^{4n}\cdot 10^{2}[/tex]
[tex]\color{red}\large \boxed{\bf A = (2^{2n}\cdot 10)^{2}\longrightarrow patrat~perfect}[/tex]
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