Question

giải PT nghiệm nguyên \(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{6xy}=\dfrac{1}{6}\)

Answer 1

ĐKXĐ: \(xy\ne0\)

\(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{6xy}=\dfrac{1}{6}\)

\(\Rightarrow6x+6y+1=xy\)

\(\Leftrightarrow xy-6x-6y+36=37\)

\(\Leftrightarrow x\left(y-6\right)-6\left(y-6\right)=37\)

\(\Leftrightarrow\left(x-6\right)\left(y-6\right)=37\)

\(\Rightarrow\left(x-6;y-6\right)=\left(-37;-1\right);\left(-1;-37\right);\left(1;37\right);\left(37;1\right)\)

\(\Rightarrow\left(x;y\right)=\left(-31;5\right);\left(5;-31\right);\left(7;43\right);\left(43;7\right)\)