Question

Tìm x thuộc z Sao cho 12-x chi hết cho 8-x

Answer 1

\(12-x⋮8-x\)

\(\Rightarrow4+\left(8-x\right)⋮8-x\)

Do \(4+\left(8-x\right)⋮8-x\)và \(8-x⋮8-x\)nên \(4⋮8-x\)

\(\Rightarrow8-x\inƯ\left(4\right)=\left\{-4;-2;-1;1;2;4\right\}\)

\(\Rightarrow x=\left\{12;10;9;7;6;4\right\}\)

Answer 2

\(\frac{12-x}{8-x}=\frac{8-x+4}{8-x}=\frac{8-x}{8-x}+\frac{4}{8-x}=1+\frac{4}{8-x}\)

=> 8-x \(\in\) Ư(4) = {-1,-4,1,4}

Ta có bảng :

8-x	-1	-4	1	4
x	9	12	7	4

Vậy x = {4,7,9,12}

Answer 3

Làm lại

\(\frac{12-x}{8-x}=\frac{8-x+4}{8-x}=\frac{8-x}{8-x}+\frac{4}{8-x}=1+\frac{4}{8-x}\)

=> \(8-x\inƯ\left(4\right)=\left\{-1,-2,-4,1,2,4\right\}\)

Ta có bảng :

8-x	-1	-2	-4	1	2	4
x	9	10	12	7	6	4

Vậy x = {4,6,7,9,10,12}