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Re: HSC 2015 2U Marathon 5x^{2} + 10x +\frac{1}{2} =0 \\ \\ \alpha +\beta =\frac{-10}{5} = -2 \\ \alpha \beta =\frac{\frac{1}{2}}{5} = \frac{1}{10} \\ $Now, sub in for result.$

Re: HSC 2015 2U Marathon \frac{\alpha^{2}+\beta ^{2}}{\alpha} + \frac{\alpha ^{2}+\beta ^{2}}{\beta } = \frac{\alpha ^{3}+\beta ^{3} +\alpha \beta \left ( \alpha +\beta \right )}{\alpha \beta } \\ \\ $Now, $ \\ \begin{align*}\left ( \alpha +\beta \right )^{3} &= \left ( \alpha +\beta...