Question

Tìm x,y thuộc Z sao cho
             4xy-3x+2y=15

Answer 1

\(4xy-3x+2y=15\)

\(\Leftrightarrow x\left(4y-3\right)+2y=15\)

\(\Leftrightarrow2x\left(4y-3\right)+4y=30\)

\(\Leftrightarrow2x\left(4y-3\right)+4y-3=27\)

\(\Leftrightarrow\left(2x+1\right)\left(4x-3\right)=27\)

Ta có bảng sau: 

2x + 1	27	1	-1	-27	3	9	-3	-9
4y - 3	1	27	-27	-1	9	3	-9	-3
x	13	0	-1	-14	1	4	-2	-5
y	1	\(\dfrac{15}{2}\)	-6	\(\dfrac{1}{2}\)	3	\(\dfrac{3}{2}\)	\(-\dfrac{3}{2}\)	0

Vậy: \(\left(x;y\right)=\left\{\left(13;1\right);\left(-1;-6\right);\left(1;3\right);\left(-5;0\right)\right\}\)

Answer 2

4xy - 3x + 2y = 15

(4xy + 2y) - 3x = 15

2y(2x + 1) - 3x = 15

4y(2x + 1) - 6x = 30

4y(2x + 1) - 6x - 3 = 30 - 3

4y(2x + 1) - 3(2x + 1) = 27

(2x + 1)(4y - 3) = 27

*) TH1: 2x + 1 = -27; 4y - 3 = -1

+) 2x + 1 = -27

2x = -28

x = -14

+) 4y - 3 = -1

4y = 2

y = 1/2 (loại)

*) TH2: 2x + 1 = -9; 4y - 3 = -3

+) 2x + 1 = -9

2x = -10

x = -5

+) 4y - 3 = -3

4y = 0

y = 0

*) TH3: 2x + 1 = -1; 4y - 3 = -27

+) 2x + 1 = -1

2x = -2

x = -1

+) 4y - 3 = -27

4y = -24

y = -6

*) TH4: 2x + 1 = -3; 4y - 3 = -9

+) 2x + 1 = -3

2x = -4

x = -2

+) 4y - 3 = -9

4y = -6

y = -3/2 (loại)

*) TH5: 2x + 1 = 1; 4y - 3 = 27

+) 2x + 1 = 1

2x = 0

x = 0

+) 4y - 3 = 27

4y = 30

y = 15/2 (loại)

*) TH6: 2x + 1 = 3; 4y - 3 = 9

+) 2x + 1 = 3

2x = 2

x = 1

+) 4y - 3 = 9

4y = 12

y = 3

*) TH7: 2x + 1 = 9; 4y - 3 = 3

+) 2x + 1 = 9

2x = 8

x = 4

+) 4y - 3 = 3

4y = 6

y = 3/2 (loại)

*) TH8: 2x + 1 = 27; 4y - 3 = 1

+) 2x + 1 = 27

2x = 26

x = 13

+) 4y - 3 = 1

4y = 4

y = 1

Vậy ta tìm được các cặp giá trị (x; y) thỏa mãn:

(13; 1); (1; 3); (-1; -6); (-5; 0)