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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 6: Tìm số nguyên x,y biết: xy + x – 3y – 3 = 15

Tháng Tư 24, 2022 Toán học 2 Comments 0 views

Toán Lớp 6: Tìm số nguyên x,y biết: xy + x – 3y – 3 = 15

Comments ( 2 )

  1. quynhthanhnhu
    quynhthanhnhu
    24 Tháng Tư, 2022 at 9:15 sáng
    Reply
    \xy + x – 3y – 3 = 15
    \x (y + 1) – 3 (y + 1) = 15
     \(y + 1) (x – 3) = 15
    \⇒ y + 1; x – 3 ∈ Ư(15)
    \⇒ y + 1, x – 3 ∈ {± 1; ± 3; ± 5; ± 15}
    Ta có bảng sau: (hình ở dưới)
    – Vậy \(x, y) ∈ {(2; -16); (4; 14); (0; -6); (6; 4); (-2; -4); (8; 2); (-12; -2); (18; 0)}

    toan-lop-6-tim-so-nguyen-y-biet-y-3y-3-15

  2. ngoclandiep
    ngoclandiep
    24 Tháng Tư, 2022 at 9:15 sáng
    Reply
    xy + x – 3y – 3 = 15
    ⇒ x . ( y + 1 ) – ( 3y + 3 ) = 15
    ⇒ x . ( y + 1 ) – 3 . ( y + 1 ) = 15
    ⇒ ( y + 1 ) . ( x – 3 ) = 15
    Vì x , y ∈ Z ⇒ y + 1 , x – 3 ∈ Z
    Ta có bảng sau :
    \begin{array}{|c|c|c|}\hline \text{x – 3}&\text{1}&\text{3}&\text{5}&\text{- 1}&\text{- 3}&\text{- 5}&\text{15}&\text{- 15}\\\hline \text{y + 1}&\text{15}&\text{5}&\text{3}&\text{- 15}&\text{- 5}&\text{- 3}&\text{1}&\text{- 1}\\\hline \text{x}&\text{4}&\text{6}&\text{8}&\text{2}&\text{0}&\text{- 2}&\text{18}&\text{- 12}\\\hline \text{y}&\text{14}&\text{4}&\text{2}&\text{- 16}&\text{- 6}&\text{- 4}&\text{0}&\text{- 2}\\\hline\end{array}
    Vậy ; ( x ; y ) ∈ { ( 4 ; 14 ) ; ( 6 ; 4 ) ; ( 8 ; 2 ) ; ( 2 ; – 16 ) ; ( 0 ; – 6 ) ; ( – 2 ; – 4 ) ; ( 18 ; 0 ) ; ( – 12 ; 2 ) }

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222-9+11+12:2*14+14 = ? ( )

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