48: Theo Vi-et, ta có: \(x_1+x_2=-\frac{b}{a}=-\frac53;x_1x_2=\frac{c}{a}=\frac{-6}{3}=-2\)
\(y_1+y_2=x_1+x_2+\frac{1}{x_1}+\frac{1}{x_2}\)
\(=x_1+x_2+\frac{x_1+x_2}{x_1x_2}=-\frac53+\left(-\frac53\right):\left(-2\right)=\frac{-5}{3}+\frac56=\frac{-10}{6}+\frac56=-\frac56\)
\(y_1\cdot y_2=\left(x_1+\frac{1}{x_2}\right)\left(x_2+\frac{1}{x_1}\right)\)
\(=x_1x_2+1+1+\frac{1}{x_1x_2}=-2+2+\frac{1}{-2}=\frac{-1}{2}\)
Phương trình cần tìm là:
\(y^2-\left(-\frac56\right)y+\frac{-1}{2}=0\)
=>\(y^2+\frac56y-\frac12=0\)
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