Toán Lớp 6: Tìm số nguyên x biết :
3x + 4 chia hết cho x – 3
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Toán Lớp 6: Tìm số nguyên x biết :
3x + 4 chia hết cho x – 3
Comments ( 2 )
Ta có: 3x + 4 $\vdots$ x – 3
Mà x – 3 $\vdots$ x – 3
=> (3x + 4) – (x – 3)$\vdots$ x – 3
=> (3x + 4) – (3x – 9)$\vdots$ x – 3
=> 3x + 4 – 3x + 9$\vdots$ x – 3
=> 13 $\vdots$ x – 3
=> x – 3 là Ư(13)
Ta có bảng sau:
\begin{array}{|c|c|c|}\hline \text{x-3}&\text{1}&\text{-1}&\text{13}&\text{-13}\\\hline \text{x}&\text{4}&\text{2}&\text{16}&\text{-10}\\\hline\end{array}
Vậy x ∈ { 4; 2; 16; -10 }
3x + 4 \vdots x – 3
x – 3 \vdots x – 3
=> [(3x + 4) – 3(x – 3)] \vdots x – 3
=> [(3x + 4) – (3x – 9)] \vdots x – 3
=> 13 \vdots x – 3
=> x – 3 in Ư(13) = {1; -1; 13; -13}
=> x – 3 in {1; -1; 13; -13}
=> x in {4; 2; 16; -10}
Vậy x in {4; 2; 16; -10}