tìm a ,b để 1/a - 1/b = 1/a-b

\(\frac{1}{a} - \frac{1}{b} = \frac{1}{{a - b}}\)

⇔ \(\frac{{b - a}}{{ab}} = - \frac{1}{{b - a}}\)

⇔ (b – a)² = –ab

⇔ a² – ab + b² = 0

⇔ \({\left( {a - \frac{b}{2}} \right)^2} + \frac{{3{b^2}}}{4} = 0\) (*)

Ta thấy \[{\left( {a - \frac{b}{2}} \right)^2} + \frac{{3{b^2}}}{4} \ge 0,\forall a,b \in \mathbb{Z}\] nên để (*) xảy ra thì:

\(\left\{ \begin{array}{l}a - \frac{b}{2} = 0\\\frac{{3{b^2}}}{4} = 0\end{array} \right. \Leftrightarrow a = b = 0\)