Question

Tìm  x,y thuộc N biết: 

a) x . y  + 8 = x + y

b) (5x + 7) chia hết cho x - 2

c) 2x.(y - 3) = y + 2

 

Answer 1

\(xy+8=x+y\)

\(\Leftrightarrow xy-x-y+1=-7\)

\(\Leftrightarrow\left(x-1\right)\left(y-1\right)=-7=1.\left(-7\right)=\left(-1\right).7\)

\(=\left(-7\right).1=7.\left(-1\right)\)

Answer 2

\(5x+7⋮x-2\)

\(\Rightarrow5\left(x-2\right)+17⋮x-2\)

\(\Rightarrow17⋮x-2\)

\(\Leftrightarrow x-2\in\left\{1;-1;17;-17\right\}\)

\(\Leftrightarrow x\in\left\{3;1;19\right\}\)

Answer 3

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

\(\Leftrightarrow2x\left(y-3\right)=\left(y-3\right)+5\)

\(\Leftrightarrow\left(2x-1\right)\left(y-3\right)=5=\left(-1\right).\left(-5\right)=1.5\)

\(=\left(-5\right).\left(-1\right)=5.1\)