Question

tìm các cặp số nguyên (a,b) sao cho

a,(x-2).(y+3)=5

b,xy-6x-3y=7

c,\(\dfrac{a}{2}\)-\(\dfrac{1}{b}\)=\(\dfrac{3}{4}\)

d,\(\dfrac{a-5}{6}\)-\(\dfrac{1}{b-2}\)=\(\dfrac{1}{8}\)

Answer 1

\(\left(x-2\right)\left(y+3\right)=5\)

\(\Rightarrow x-2;y+3\inƯ\left(5\right)\)

\(Ư\left(5\right)=\left\{\pm1;\pm5\right\}\)

Xét ước

\(xy-6x-3y=7\)

\(\Rightarrow xy-6x-3y+18=25\)

\(\Rightarrow x\left(y-6\right)-3\left(y-6\right)=25\)

\(\Rightarrow\left(x-3\right)\left(y-6\right)=25\)

Xét ước

\(\dfrac{a}{2}-\dfrac{1}{b}=\dfrac{3}{4}\)

\(\Rightarrow\dfrac{1}{b}=\dfrac{3}{4}+\dfrac{a}{2}\)

\(\Rightarrow\dfrac{1}{b}=\dfrac{3}{4}+\dfrac{2a}{4}\)

\(\Rightarrow\dfrac{1}{b}=\dfrac{3+2a}{4}\)

\(\Rightarrow b\left(3+2a\right)=4\)

Xét ước