Toán Lớp 6: Tìm x,y ∈ N: 2xy + x – 6y = 21
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Toán Lớp 6: Tìm x,y ∈ N: 2xy + x – 6y = 21
Comments ( 2 )
2xy + x – 6y = 21
⇒ 2x.(y+1) – (6y+6) = 15
⇒ 2x.(y+1) – 6.(y+1)=15
⇒ (y+1) . (2x-6)=15
y ∈ N nên y+1 ≥ 1
Mà 15=1 .15=3.5
2x – 6 là số chẵn với x ∈ N
Vậy không tìm được x;y thoả mãn
Giải đáp:
( x ; y ) = ( 5 ; 4 ) ; ( 9 ; 1 ) ; ( 21 ; 0 )
Lời giải và giải thích chi tiết:
2xy + x – 6y = 21
=> 2xy + x – 6y – 3 = 21 – 3
=> x . ( 2y + 1 ) – 3 . ( 2y + 1 ) = 18
=> ( x – 3 )( 2y + 1 ) = 18
Ta có bảng :
$\begin{array}{|c|c|c|}\hline\text{x – 3}&\text{1}&\text{- 1}&\text{2}&\text{- 2}&\text{3}&\text{- 3}&\text{6}&\text{- 6}&\text{9}&\text{- 9}&\text{18}&\text{- 18}\\\hline \text{2y + 1}&\text{18}&\text{- 18}&\text{9}&\text{- 9}&\text{6}&\text{- 6}&\text{3}&\text{- 3}&\text{2}&\text{- 2}&\text{1}&\text{- 1}\\\hline\end{array}$
Nên :
$\begin{array}{|c|c|c|}\hline\text{x}&\text{4}&\text{2}&\text{5}&\text{1}&\text{6}&\text{0}&\text{9}&\text{- 3}&\text{12}&\text{- 6}&\text{21}&\text{- 15}\\\hline \text{y}&\text{$\frac{17}{2}$ }&\text{$\frac{-19}{2}$ }&\text{4 }&\text{- 5 }&\text{$\frac{5}{2}$ }&\text{$\frac{- 7}{2}$ }&\text{1 }&\text{- 2 }&\text{$\frac{1}{2}$ }&\text{$\frac{- 3}{2}$ }&\text{0 }&\text {- 1}\\\hline\end{array}$
Mà x ; y ∈ NN .
=> ( x ; y ) = ( 5 ; 4 ) ; ( 9 ; 1 ) ; ( 21 ; 0 )
Vậy ( x ; y ) = ( 5 ; 4 ) ; ( 9 ; 1 ) ; ( 21 ; 0 )