Question

Tìm \(x,y\in Z\),biết \(x,y\ne0\) và \(\dfrac{7}{15x}+\dfrac{9}{10y}=\dfrac{2}{5}-\dfrac{359}{30xy}\)

Answer 1

Ta có: \(\dfrac{7}{15x}+\dfrac{9}{10y}=\dfrac{2}{5}-\dfrac{359}{30xy}\)

\(\Leftrightarrow\dfrac{14}{30xy}+\dfrac{27}{30xy}=\dfrac{12xy}{30xy}-\dfrac{359}{30xy}\)

\(\Leftrightarrow\dfrac{41}{30xy}=\dfrac{12xy-359}{30xy}\)

\(\Rightarrow12xy-359=41\)

\(\Rightarrow12xy=400\)

\(\Rightarrow xy=\dfrac{100}{3}\)

Vì \(x,y\in Z\) mà \(xy=\dfrac{100}{3}\)

\(\Rightarrow\) Phương trình vô nghiệm.