Răspuns:
Explicație pas cu pas:
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[tex]\it \sqrt{5^{2n+1}\cdot9^{n+1}+25^n\cdot3^{2n+2}\cdot11}=\sqrt{5\cdot5^{2n}\cdot9\cdot3^{2n}+5^{2n}\cdot9\cdot3^{2n}\cdot11}=\\ \\ \\ =\sqrt{15^{2n}(45+99)}=\sqrt{(15^n)^2\cdot144}=12\cdot15^n\in\mathbb{N}[/tex]
