If \( \alpha, \beta \) are the roots of the equation \( 3 x^{2}-6 x+4=0 \), evaluate \( \left(\f...
If \( \alpha, \beta \) are the roots of the equation \( 3 x^{2}-6 x+4=0 \), evaluate \( \left(\frac{\alpha^{2}}{\beta}+\frac{\beta^{2}}{\alpha}\right)+\left(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\right)+2\left(\frac{1}{\alpha}+\frac{1}{\beta}\right)+3 \alpha \beta \).
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