Question

\(\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{617}\)

Answer 1

\(\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{617}\)

\(\Rightarrow\dfrac{x+y}{xy}=\dfrac{1}{617}\)

\(\Rightarrow617\left(x+y\right)=xy\)

\(\Rightarrow617x+617y=xy\)

\(\Rightarrow617x+617y-xy+617^2=617^2\)

\(\Rightarrow\left(y-617\right)\left(x-617\right)=617^2\)

\(\Rightarrow\left[{}\begin{matrix}x-617=617\\y-617=617\end{matrix}\right.\)

\(\Rightarrow x=y=1234\)