Câu hỏi của Bùi Nguyễn Quỳnh Ngân

Question

tìm các số tự nhiên x sao cho x + 80 chia hết cho x+ 3 , 2x +65 chia hết cho x + 1

Trần Thu Hà · Accepted Answer

$a,$$x+80⋮x+3$$\Rightarrow$$\left(x+3\right)+77⋮x+3$Vì $x+3⋮x+3$nên $77⋮x+3$$\Rightarrow$$x+3\inƯ\left(77\right)$$\Rightarrow$$x+3\in\left\{1;-1;7;-7;11;-11;77;-77\right\}$$\Rightarrow$$x\in\left\{-2;-4;4;-10;8;-14;74;-80\right\}$mà $x\in N$nên $x\in\left\{4;8;74\right\}$$b,$$2x+65⋮x+1$$\Rightarrow$$2\left(x+1\right)+63⋮x+1$Vì $x+1⋮x+1$nên $2\left(x+1\right)⋮x+1$Do đó, $63⋮x+1$$\Rightarrow$$x+1\inƯ\left(63\right)$$\Rightarrow$$x+1\in\left\{1;-1;3;-3;7;-7;9;-9;21;-21;63;-63\right\}$$\Rightarrow$$x\in\left\{0;-2;2;-4;6;-8;8;-10;20;-22;62;-64\right\}$mà $x\in N$nên $x\in\left\{0;2;6;8;20;62\right\}$Câu trả lời: $a,$$x+80⋮x+3$$\Rightarrow$$\left(x+3\right)+77⋮x+3$Vì $x+3⋮x+3$nên $77⋮x+3$$\Rightarrow$$x+3\inƯ\left(77\right)$$\Rightarrow$$x+3\in\left\{1;-1;7;-7;11;-11;77;-77\right\}$$\Rightarrow$$x\in\left\{-2;-4;4;-10;8;-14;74;-80\right\}$mà $x\in N$nên $x\in\left\{4;8;74\right\}$$b,$$2x+65⋮x+1$$\Rightarrow$$2\left(x+1\right)+63⋮x+1$Vì $x+1⋮x+1$nên $2\left(x+1\right)⋮x+1$Do đó, $63⋮x+1$$\Rightarrow$$x+1\inƯ\left(63\right)$$\Rightarrow$$x+1\in\left\{1;-1;3;-3;7;-7;9;-9;21;-21;63;-63\right\}$$\Rightarrow$$x\in\left\{0;-2;2;-4;6;-8;8;-10;20;-22;62;-64\right\}$mà $x\in N$nên $x\in\left\{0;2;6;8;20;62\right\}$

2x+3	1	2	7	14
x	-1 (loại)	\(\frac{-1}{2}\) (loại)	2	\(\frac{11}{2}\) (loại)

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x-1	1	2	3	6
x	2	3	4	7

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