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Math Help - Surds

  1. #1
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    Surds

    Given that [a - 6 sqrt(5)] x [2 + b sqrt(5)] = -82, where a and b are rational numbers, find the possible values of a and b
    [Ans = a = 4, b =3, or a = -45, b = -4/15]

    I have expanded the expression to obtain
    2a + sqrt 5 (ab-12) - 30 b = 82, but I don't know how to proceed to get simulataneous equations to solve for a and b.

    Please help.
    Thanks
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  2. #2
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    Quote Originally Posted by Drdj View Post
    Given that [a - 6 sqrt(5)] x [2 + b sqrt(5)] = -82, where a and b are rational numbers, find the possible values of a and b
    [Ans = a = 4, b =3, or a = -45, b = -4/15]

    I have expanded the expression to obtain
    2a + sqrt 5 (ab-12) - 30 b = 82, but I don't know how to proceed to get simulataneous equations to solve for a and b.

    Please help.
    Thanks
    (a - 6 \sqrt{5}) \cdot (2 + b \sqrt{5}) = 2a + (ab-12)\sqrt{5} - 30b = -82

    2a - 30b = -82

    ab-12 = 0
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  3. #3
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    We need to know that "a and b are rational numbers" in order to be certain that (ab- 12)\sqrt{5} is not a rational number and so we can so we must have (ab- 12)\sqrt{5}= 0.
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