Tìm x;y thuộc Z biết : 6xy-4x+3y=-53

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1. `6xy – 4x + 3y = -53`

   `⇔ 3y(2x + 1) – 4x -2 = -55`

   `⇔ 3y(2x + 1) – 2(2x + 1) = -55`

   `⇔ (2x + 1)(3y-2)=-55`

   `x; y ∈ Z ⇒ 2x + 1; 3y-2 ∈ Ư(-55) = {±1; ±5; ±11; ±55}`

   $\text{Ta có bảng sau:}$

   $\text{Vậy (x; y) = (2; -3); (5; -1); (-1; 19); (-28; 1)}$

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2. `6xy-4x+3y=-53`

   `⇔6xy-4x+3y+53=0`

   `⇔2x(3y-2)+(3y-2)+55=0 `

   `⇔(2x+1)(3y-2)=-55`

   TH1:

   `2x+1=1;3y-2=-55`

   `⇔2x=0;3y=-53 `

   `⇔ y∉Z`

   TH2:

   `2x+1=-55;3y-2=1`

   `⇔2x=-56;3y=3`

   `⇔x=-28;y=1`

   TH3:

   `2x+1=-1;3y-2=55 `

   `⇔2x=-2;3y=57`

   `⇔x=-1;y=19`

   TH4:

   `2x+1=55;3y-2=-1`

   `⇔2x=54;3y=1`

   `⇔y∉Z`

   TH5:

    `2x+1=-11;3y-2=5 `

   `⇔2x=-12;3y=7`

   `⇔y∉Z`

   TH6:

   `2x+1=5;3y-2=-11`

   `⇔2x=4;3y=-9`

   `⇔x=2;y=-3`

   TH7:

   `2x+1=11;3y-2=-5`

   `⇔2x=10;3y=-3`

   `⇔x=5;y=-1`

   TH8: 

   `2x+1=-5;3y-2=11`

   `⇔2x=-6;3y=13`

   `⇔y∉Z`

   Vậy `(x;y)=(5;-1) ; (2;-3) ; (-1;19) ; (-28;1)`

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