Toán Lớp 6: Tìm x , y ∈ ZZ biết :
( 2x + 1 ) ( 2y – 1 ) = -35
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Toán Lớp 6: Tìm x , y ∈ ZZ biết :
( 2x + 1 ) ( 2y – 1 ) = -35
Comments ( 2 )
Ta có: (2x+1)(2y-1) = -35
=> x;y in Ư(-35) = {±1;±5;±7;±35}
Ta có bảng sau:
$\begin{array}{|c|c|c|}\hline \text{2x+1}&\text{1}&\text{-1}&\text{5}&\text{-5}&\text{7}&\text{-7}&\text{35}&\text{-35}\\\hline \text{2x}&\text{0}&\text{-2}&\text{4}&\text{-6}&\text{6}&\text{-8}&\text{34}&\text{-36}\\\hline \text{x}&\text{0}&\text{-1}&\text{2}&\text{-3}&\text{3}&\text{-4}&\text{17}&\text{-18}\\\hline \text{2y-1}&\text{-35}&\text{35}&\text{-7}&\text{7}&\text{-5}&\text{5}&\text{-1}&\text{1}\\\hline \text{2y}&\text{-34}&\text{36}&\text{-6}&\text{8}&\text{-4}&\text{6}&\text{0}&\text{2}\\\hline \text{y}&\text{-17}&\text{18}&\text{-3}&\text{4}&\text{-2}&\text{3}&\text{0}&\text{1}\\\hline\end{array}$
text\{Vậy (x;y) ∈ {(0;-17),(-1;18),(2;-3),(-3;4),(3;-2),(-4;3),(17;0),(-18;1)}}
Tham khảo:
( 2x + 1 ) ( 2y – 1 ) = -35
=> 2x + 1; 2y – 1 \in Ư(-35) = { -35; -7; -5; -1; 1; 5; 7; 35 }
Ta có bảng:
$\begin{array}{|c|c|c|}\hline {2x + 1}&{-35}&{-7}&{-5}&{-1}&{1}&{5}&{7}&{35}\\\hline {2y – 1}&{1}&{5}&{7}&{35}&{-35}&{-7}&{-5}&{-1}\\\hline {x}&{-18}&{-4}&{-3}&{-1}&{0}&{2}&{3}&{17}\\\hline {y}&{1}&{3}&{4}&{18}&{-17}&{-3}&{-2}&{0}\\\hline\end{array}$
#Sad