Ta có: \(3x^2-5x+2=0\)
\(\Leftrightarrow3x^2-3x-2x+2=0\)
\(\Leftrightarrow3x\left(x-1\right)-2\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(3x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\3x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\3x=2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x_1=1\\x_2=\frac{2}{3}\end{matrix}\right.\)
Ta có: \(\frac{1}{x_1}-\frac{1}{x_2}\)
\(=\frac{1}{1}-\frac{1}{\frac{2}{3}}=1-1\cdot\frac{3}{2}=1-\frac{3}{2}=-\frac{1}{2}\)
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