Question

Cum se rezolva aceasta problema. Vreau raspunsul cu toti pasi daca se poate.

Answer 1

 

$\displaystyle\bf\\1\\\\\frac{(n+2)!}{n!}=56\\\\(n+2)!=n!(n+1)(n+2)\\\\\implies~\frac{(n+2)!}{n!}=\frac{n!(n+1)(n+2)}{n!}\\\\Rezolvare\\\\\\\frac{(n+2)!}{n!}=56\\\\\\\frac{n!(n+1)(n+2)}{n!}=56\\\\Simplificam~pe~n!\\\\(n+1)(n+2)=56\\\\(n+1)~si~(n+2)~sunt~numere~consecutive.\\Descompunem~numarul~56~in~produs~de~numere~consecutive.\\\\56=7\times8\\\\(n+1)(n+2)=7\times8\\\\\implies~n+1=7\\\\n=7-1\\\\n=\boxed{\bf6}$