Cerinta:
"Aratati ca numarul B = (5⁶¹ + 5⁶² + 5⁶⁰) · 961 este cub perfect."
Rezolvare:
[tex]\bf (5^{61}+ 5^{62}+5^{60})\cdot 961=[/tex]
[tex]\bf (5^{60}+ 5^{61}+5^{62})\cdot 961=[/tex]
[tex]\bf 5^{60} \cdot (5^{60-60}+ 5^{61-60}+5^{62-60})\cdot 31 \cdot 31=[/tex]
[tex]\bf 5^{60}\cdot (5^{0}+ 5^{1}+5^{2}) \cdot 31^{2}=[/tex]
[tex]\bf 5^{60}\cdot (1+ 5+25})\cdot 31^{2}=[/tex]
[tex]\bf 5^{60}\cdot 31 \cdot 31^{2} =[/tex]
[tex]\bf 5^{60}\cdot 31^{2+1}=[/tex]
[tex]\bf5^{60}\cdot 31^{3}=[/tex]
[tex]\boxed{\bf (5^{20}\cdot 31)^{3} =>\: \text{\bf este cub perfect}}[/tex]
