Question

Tìm x,y nguyên

a)xy-x-y=2

b)xy-3x+5y=22

c)3xy-x-y=1

d)x2-2x=y2+2

bn nào giải đc câu nào thì giải nha,mik tik

Answer 1

a) \(xy-x-y=2\)
\(\Rightarrow x\left(y-1\right)-\left(y-1\right)=3\)
\(\Rightarrow\left(x-1\right)\left(y-1\right)=3\)
Ta có :
\(x-1=1;y-1=3\Rightarrow x=2;y=4\)
\(x-1=3;y-1=1\Rightarrow x=4;y=2\)
\(x-1=-1;y-1=-3\Rightarrow x=0;y=-2\)
\(x-1=-3;y-1=-1\Rightarrow x=-2;y=0\)

b) \(xy-3x+5y=22\)
\(\Rightarrow x\left(y-3\right)+5y=22\)
\(\Rightarrow x\left(y-3\right)+5\left(y-3\right)+15=22\)
\(\Rightarrow x\left(y-3\right)+5\left(y-3\right)=7\)
\(\Rightarrow\left(y-3\right)\left(x+5\right)=7\)
Ta có
\(y-3=1;x+5=7\Rightarrow y=4;x=2\)
\(y-3=7;x+5=1\Rightarrow y=10;x=-4\)
\(y-3=-1;x+5=-7\Rightarrow y=2;x=-12\)
\(y-3=-7;x+5=-1\Rightarrow y=-4;x=-6\)

P/s: ( Còn 2 bài đó làm tương tự )