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Math Help - radicals

  1. #1
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    radicals

    How to solve this:

    -3 √(6x+5) = -9

    Answer key (2/3)

    Do we use conjugate of -3 √(6x+5)? If so, what is the conjugate of -3 √(6x+5)?

    example: The conjugate of (x + √y) is (x - √y).

    I don't think the conjugate of -3 √(6x+5) is -3 √(6x-5) since the above example has 2 terms, that is x and √y while -3 √(6x+5) is only 1 term.

    I don't know how to solve this. Please help.

    Thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by shenton View Post
    How to solve this:

    -3 √(6x+5) = -9

    Answer key (2/3)
    You start by squaring to get:

    <br />
\left[ -3 \sqrt{6x+5}\right]^2 = (-9)^2<br />

    which simplifies to:

    <br />
9 (6x+5) = 9^2<br />

    further simplification gives:

    <br />
6x = 4<br />

    which si,plifies further to x=2/3.

    Now as we squared the original equation we need to check that
    any solution we subsequently find satisfies the original equation
    as squaring can introduce spurious solutions. But in this case there
    is no problem and x=2/3 is the solution.

    RonL
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  3. #3
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    Thanks for the help!
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