Question

ARATA CA NUMERELE SUNT NATURALE.
XYZXYZ SUPRA 1001.
XYZ---(X+Y+Z) SUPRA 9
AM NEVOIE DE RASPUNS URGENT!!!!​

Answer 1

 

$\displaystyle\bf\\\\ a)\\\\\frac{~\overline{xyzxyz}~}{1001}=\frac{100000x+10000y+1000z+100x+10y+z}{1001}=\\\\=\frac{(100000x+100x)+(10000y+10y)+(1000z+z)}{1001}=\\\\=\frac{(100100x)+(10010y)+(1001z)}{1001}=\\\\=\frac{1001\Big(100x+10y+z\Big)}{1001}=100x+10y+z=\overline{xyz}~~\in~~N\\\\\\b)\\\\\frac{~\overline{xyz}-(x+y+z)}{9}=\frac{~100x+10y+z-x-y-z}{9}=\\\\=\frac{~100x-x+10y-y+z-z}{9}=\\\\=\frac{~99x+9y}{9}=\frac{~9(11x+y)}{9}=11x+y~\in~N$