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10 October, 17:09

if alpha and beta are the roots of the equation 3x^2-9x+2=0 find the values of: (I) alpha * beta + alpha^2 * beta. (ii) alpha^2-alpha*beta+beta^2

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  1. 10 October, 17:32
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    Step-by-step explanation:

    The question did not state if alpha>beta or alpha
    3x²-9x+2=0

    x = ( - (-9) ± √ (-9) ²-4 * (3) * (2)) / (2*3)

    x = (9 + √57) / 6 or x = (9 - √57) / 6 (alpha and beta) or (beta and alpha)

    (I) alpha (a) * beta (b) + alpha² * beta = ab (1+a)

    = ((9 + √57) / 6) ((9 - √57) / 6) (1 + (9 ± √57))

    = ((9² - (√57) ²) / 36) (10 ± √57)

    = (24/36) (10 ± √57)

    = 2/3 (10 ± √57) or (11.7 or 1.63)

    (ii) alpha²-alpha*beta+beta² = a² - 2ab + b² + ab = (a - b) ² + ab

    if a is alpha

    = ((9 + √57) / 6) - ((9 - √57) / 6)) + ((9 + √57) / 6) ((9 - √57) / 6))

    = √57/3 + 2/3

    = (√57 + 2) / 3

    if a is beta

    ((9 - √57) / 6) - ((9 + √57) / 6)) + ((9 - √57) / 6) ((9 + √57) / 6))

    = - √57/3 + 2/3

    = - (√57 + 2) / 3
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