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- Feb 14, 2012

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Given \(\displaystyle \alpha\) and \(\displaystyle \beta\) are roots of the equation \(\displaystyle x^2-7x+8=0\), where \(\displaystyle \alpha>\beta\). Find the value of \(\displaystyle \frac{2}{\alpha}+3\beta^2\) without solving the equation.

Hi members of the forum, I just couldn't remember where did I find this problem but as I have tried to solve for the value of the intended expression, I kind of believe this couldn't be done without actually having to solve the given equation. But I wasn't sure.

Could someone please show me how to find the value of \(\displaystyle \frac{2}{\alpha}+3\beta^2\) without solving the equation, please?

Thanks.