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

Cum Se Rezolva Aceasta Problema Vreau Raspunsul Cu Toti Pasi Daca Se Poate class=

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[tex]\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}[/tex]