Question

Se consideră mulțimea A={x aparține Z/$\frac{x + 6}{x - 1}$aparține Z}.Suma elementelor mulțimii este:a)4;
b)2;
c)0;
d)-2.
E urgent!Te rog mult!

Answer 1

 

$\displaystyle\bf\\\frac{x+6}{x-1}=\frac{x-1+1+6}{x-1}=\frac{x-1+7}{x-1}=\frac{x-1}{x-1}+\frac{7}{x-1}=1+\frac{7}{x-1}\\\\1\in Z\\\\\frac{7}{x-1}\in Z\\\\\implies~(x-1)\in D_7\\\\D_7=\{-7;~-1;~1;~7\}\\\\x-1=-7~\implies x_1=-7+1=\boxed{\bf-6}\\\\x-1=-1~\implies x_2=-1+1=\boxed{\bf0}\\\\x-1=1~\implies x_3=1+1=\boxed{\bf2}\\\\x-1=7~\implies x_4=7+1=\boxed{\bf8}\\\\x\in \{-6;~0;~2;~8\}\\\\Suma~elementelor~multimii~este:\\\\S=-6+0+2+8\\\\S=4\\\\Raspuns~corect\!:~~a)~4$