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23. Ştiind că n!=1×2×3×,.....×n, unde ne N, aflați restul împartirii:(10!+9!):(10!-9!)

A) 5
B) 3
C) 9
D) 2
E) 9! 2
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Răspuns :

 

[tex]\displaystyle\bf\\Folosim~formula:~~~10!=9!\times10\\\\Rezolvare:\\\\(10!+9!):(10!-9!)=\\\\=\frac{10!+9!}{10!-9!}=\\\\\\=\frac{9!\times10+9!}{9!\times10-9!}=\\\\\\=\frac{9!(10+1)}{9!(10-1)}=\\\\\\=\frac{(10+1)}{(10-1)}=\\\\\\=\frac{11}{9}=\\\\\\=11:9=1~rest 2\\\\Raspuns:~~\boxed{\bf Restul~impartirii~este~2\times9!~}[/tex]