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    The coefficient of x^3 in the expansion of (2+x)(3-ax)^4 is 30.
    Find the values of a.

    I can't get the right answer. could someone show me their workings?
    Ty
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    (Original post by [email protected])
    The coefficient of x^3 in the expansion of (2+x)(3-ax)^4 is 30.
    Find the values of a.

    I can't get the right answer. could someone show me their workings?
    Ty
    On use of the binomial theorem, we find that the coefficient of x^3 is

    -24a^3 + 54a^2

    We equate that to 30 and solve!

    -24a^3 + 54a^2 = 30
    => 24a^3 - 54a^2 + 30 = 0
    => 4a^3 - 9a^2 + 5 = 0
    => (a - 1)(4a^2 - 5a - 5) = 0
    => a = 1, (5/8) +/- root(105)/8

    Euclid.
 
 
 
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