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Given that \(\alpha\) and \(\beta\) are the roots of the equation \(3x^2 - 5x - 7 = 0\), find the roots of \(\alpha^2 + \beta^2 - \alpha \beta\)....



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  • The answer to the question. Hope it's understood

  • Anthony

    3x\( a^{b}2 \) - 5x - 7 = 0
    a = 3, b = -5, c = -7
    \( \alpha^{2}+ \beta^{2} - \alpha\beta
    Since (\alpha + \beta)^{2} - 2\alpha\beta is the same as \alpha^{2} + \beta^{2}
    Then ( \alpha + \beta )^{2} - 2\alpha\beta - \alpha\beta
    ( \alpha + \beta )^{2} - 3\alpha\beta

    \alpha + \beta = \cfrac{-b}{a}, \cfrac{5}{3}
    \alpha\beta = \cfrac{c}{a}, \cfrac{-7}{3}
    \therefore (\cfrac{5}{3})^{2} - (3
    \times -\cfrac{7}{3})
    \cfrac{25}{9} + 7
    \frac{25 + 63}{9} = \cfrac{88}{9} \)

    1. Please can you solve it and snap it... I do not understand it like this

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