Question

[Haibara Ai]

Gọi (x₀,y₀) ( với x₀,y₀ đều là số nguyên thỏa mãn: \(\dfrac{3}{x}\)+\(\dfrac{y}{3}=\dfrac{5}{6}\).. Để \(x_0+y_0\) lớn nhất thì khi đó \(x_0-y_0=...\)

Answer 1

[Lightning Farron]

\(\dfrac{3}{x}+\dfrac{y}{3}=\dfrac{5}{6}\Leftrightarrow\dfrac{9}{3x}+\dfrac{xy}{3x}=\dfrac{5}{6}\)

\(\Leftrightarrow\dfrac{xy+9}{3x}=\dfrac{5}{6}\Leftrightarrow6\left(xy+9\right)=5\cdot3x\)

\(\Leftrightarrow6xy+54=15x\)\(\Leftrightarrow6xy-15x=-54\)

\(\Leftrightarrow3x\left(2y-5\right)=-54\)

\(\Leftrightarrow x\left(2y-5\right)=-18\)