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Ta có:
\(Ư\left(35\right)=\left\{\pm1;\pm5;\pm7;\pm35\right\}\\ \Rightarrow\left(2x+1\right),\left(2y-3\right)\in\left\{\left(5,7\right);\left(7,5\right);\left(-5;-7\right);\left(-7,-5\right);\left(1;35\right);\left(35,1\right);\left(-1,-35\right);\left(-35,-1\right)\right\}\\ \Rightarrow\left(x,y\right)\in\left\{\left(2,5\right);\left(3,4\right);\left(-3,-2\right);\left(-4,-1\right);\left(0,19\right);\left(17,2\right);\left(-1,-16\right);\left(-18,1\right)\right\}\)
(2x - 1)(2y + 1) = -35
=> -35 chia hết cho 2x - 1
=> 2x - 1 thuộc {1; -1; 5; -5; 7; -7; -35; 35}
Ta có bảng:
2x - 1 | 1 | -1 | 5 | -5 | 7 | -7 | 35 | -35 |
2x | 2 | 0 | 6 | -4 | 8 | -6 | 36 | -34 |
x | 1 | 0 | 3 | -2 | 4 | -3 | 18 | -17 |
2y + 1 | -35 | 35 | -7 | 7 | -5 | 5 | -1 | 1 |
2y | -36 | 34 | -8 | 6 | -6 | 4 | -2 | 0 |
y | -18 | 17 | -4 | 3 | -3 | 2 | -1 | 0 |
Vậy...
\(\Leftrightarrow\left(4x-2\right)y+2x-1=-35\)
\(\Rightarrow\left(4x-2\right)y+2x-\left(-35\right)-1=0\)
\(\Rightarrow2\left(\left(2x-1\right)y+x+17\right)=0\)
\(\Rightarrow2x-1=0\)
\(\Rightarrow2x=1\)
=>x=0,5 hoặc \(\frac{1}{2}\)
\(\Rightarrow2y+1=0\)
=>2y=-1
=>y=-0,5 hoặc \(-\frac{1}{2}\)
vậy x=0,5 hoặc \(\frac{1}{2}\); y=-0,5 hoặc \(-\frac{1}{2}\)
\(\left(2x-1\right)\left(2y-1\right)=-35\)
\(\Rightarrow\left(2x-1\right)\left(2y-1\right)=\left(-1\right).35=35.\left(-1\right)=1.\left(-35\right)=\left(-35\right).1=5.\left(-7\right)=\left(-7\right).5=\left(-5\right).7=7.\left(-5\right)\)
Ta có bảng sau:
\(2x-1\) | \(-1\) | \(35\) | \(1\) | \(-35\) | \(5\) | \(-7\) | \(-5\) | \(7\) |
\(2y-1\) | \(35\) | \(-1\) | \(-35\) | \(1\) | \(-7\) | \(5\) | \(7\) | \(-5\) |
\(x\) | \(0\) | \(18\) | \(1\) | \(-17\) | \(3\) | \(-3\) | \(-2\) | \(4\) |
\(y\) | \(18\) | \(0\) | \(-17\) | \(1\) | \(-3\) | \(3\) | \(4\) | \(-2\) |
Vậy \(\left(x;y\right)=\left\{\left(0;18\right);\left(18;0\right);\left(1;-17\right);\left(-17;1\right);\left(3;-3\right);\left(-3;3\right);\left(-2;4\right);\left(4;-2\right)\right\}\)
a: \(\left(x,y\right)\in\left\{\left(1;-21\right);\left(-21;1\right);\left(-1;21\right);\left(21;-1\right);\left(3;-7\right);\left(-7;3\right);\left(-3;7\right);\left(7;-3\right)\right\}\)
b: \(\Leftrightarrow\left(x,y-3\right)\in\left\{\left(1;-6\right);\left(-6;1\right);\left(2;-3\right);\left(-3;2\right);\left(-2;3\right);\left(3;-2\right);\left(6;-1\right);\left(-1;6\right)\right\}\)
hay \(\left(x,y\right)\in\left\{\left(1;-3\right);\left(-6;4\right);\left(2;0\right);\left(-3;-1\right);\left(-2;6\right);\left(3;1\right);\left(6;2\right);\left(-1;9\right)\right\}\)
TH1: 2x-1 = -35
=> 2x= -35+1 = -34
=> x= -34:2 = -17
TH2: 2y+1 = -35
=> 2y = -35-1 = -36
=> y= -36:2 = -18
duyệt đi