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Math Help - evaluation

  1. #1
    ADY
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    evaluation

    when c=-7 and d=4

    \sqrt{d} - dc^2

    \sqrt{4} - 4 x (-7)^2

    2 - 4 x (-7)^2 = -194

    this right?
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by ADY View Post
    when c=-7 and d=4

    \sqrt{d} - dc^2

    \sqrt{4} - 4 x (-7)^2

    2 - 4 x (-7)^2 = -194

    this right?
    it is right but \sqrt{4}=\mp 2 since 2^2=4 and (-2)^2=4 so you will have two answers the first one you find it
    the second one

    -2-4(-7)^2=-198
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  3. #3
    ADY
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    So are you saying there are two answers?
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  4. #4
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by ADY View Post
    So are you saying there are two answers?
    yeah
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  5. #5
    ADY
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    Ok so i'm not sure what to do now then?
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  6. #6
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by ADY View Post
    Ok so i'm not sure what to do now then?
    did you know that

    (-2)^2=4
    (-4)^2=16
    (-7)^2=49

    so

    \sqrt{4}=\mp 2
    \sqrt{16}=\mp 4
    \sqrt{49}=\mp 7

    in general
    \sqrt{a^2}=\mp a a is real number

    in you question

    \sqrt{4}-4(-7)^2 have two solutions since \sqrt{4}=2 and \sqrt{4}=-2

    first one
    2-4(49)=2-196=-194

    second one

    -2-4(49)=-2-196=-198
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  7. #7
    ADY
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    Does the same apply to this formula

    a = -7, b = 4

    a - b(a + b)

    (-7) - 4((-7)+4) = 5
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  8. #8
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by ADY View Post
    Does the same apply to this formula

    a = -7, b = 4

    a - b(a + b)

    (-7) - 4((-7)+4) = 5
    it is correct
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  9. #9
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    Talking

    Quote Originally Posted by ADY View Post
    So are you saying there are two answers?
    One might say that the evaluation has two answers, but this would be incorrect.

    While one solves "x^2 = 4" for the two solution values, -2 and +2, "the" value of the square root of 4, sqrt[4], is defined to be the principal (that is, the positive real) value: sqrt[4] = 2.

    So no, there will most definitely not be two answers to this one evaluation exercise!

    \sqrt{d}\, -\, dc^2\, =\,\sqrt{4}\, -\, (4)(-7)^2

    . . . =\, 2\, -\,4(49)\, =\, 2\, -\, 196\, =\, -194

    And the above is the only answer!
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