Question

1.tìm x,y \(\in Z,biết:\)

a)xy+2x+y+11=0

b)\(\frac{1}{x}+\frac{1}{y}=\frac{1}{2}\)

Answer 1

xy+2x+y+11=0

=> x.(y+2)+y=-11

=> x.(y+2)+(y+2)= -11+2=-9

=> (x+1).(y+2)=-9

=> x+1 và y+2 thuộc Ư(-9)={1;-1;3;-3;9;-9}

Vậy....

Answer 2

\(xy+2x+y+11=0\)

\(\Rightarrow y\left(x+y\right)+2\left(x+5,5\right)=0\)

\(\Rightarrow\hept{\begin{cases}y\left(x+y\right)=0\\x+5,5=0\end{cases}\Rightarrow\hept{\begin{cases}y=0\\x=-5,5\end{cases}}}\)