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Math Help - Important question plzzzzzzz help

  1. #1
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    Important question plzzzzzzz help

    THE SOLUTION OF

    [X + (X^2-1)^1/2 / X - (X^2-1)^1/2] + [ X - (X^2-1)^1/2 / X + (X^2-1)^1/2 ] = 14

    a) +8

    b) -6

    c) + or- 2

    d) + or - 4
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Important question plzzzzzzz help

    I have a few suggestions for you to get prompt help here:

    • Use unique and descriptive topic titles.
    • Use proper bracketing symbols or better yet use \LaTeX to make your questions unambiguous.
    • Show you work so the helpers here know exactly where you are stuck.
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  3. #3
    MHF Contributor ebaines's Avatar
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    Re: Important question plzzzzzzz help

    Quote Originally Posted by sscgeek View Post
    THE SOLUTION OF

    [X + (X^2-1)^1/2 / X - (X^2-1)^1/2] + [ X - (X^2-1)^1/2 / X + (X^2-1)^1/2 ] = 14
    What you wrote is this:

     \left [ x+ \frac {\sqrt{x^2-1}} x - \sqrt {x^2-1} \right ] + \left [ x - \frac {\sqrt{x^2-1}} x + \sqrt {x^2-1} \right ] = 14

    Note that many of the terms cancel out, leaving just 2x = 14. So it seems that for the equation you wrote none of the answers are correct.
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  4. #4
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    Re: Important question plzzzzzzz help

    Hello, sscgeek!

    \text{Solve: }\: \frac{x + \sqrt{x^2-1}}{x - \sqrt{x^2-1}} + \frac{x - \sqrt{x^2-1}}{x + \sqrt{x^2-1}}\;=\;14

    . . (a)\;+8  \qquad (b)\;-6 \qquad (c)\;\pm 2 \qquad (d)\; \pm4

    We have: . \frac{(x+\sqrt{x^2-1})^2 + (x-\sqrt{x^2-1})^2} {(x-\sqrt{x^2-1})(x+\sqrt{x^2-1})} \;=\; 14

    . . \frac{(x^2 + 2x\sqrt{x^2-1} + x^2-1) + (x^2 - 2x\sqrt{x^2-1} + x^2-1)}{x^2 - (x^2-1)} \;=\;14

    . . \frac{4x^2 - 2}{1} \:=\:14 \quad\Rightarrow\quad 4x^2 \:=\:16 \quad\Rightarrow\quad x^2 \:=\:16

    . . x \:=\:\pm4 .Answer (d)
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  5. #5
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    Re: Important question plzzzzzzz help

    Interesting. Soroban's interpretation of what sscgeek wrote is quite different from ebaines' interpretation.
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  6. #6
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    Re: Important question plzzzzzzz help

    I would say that Soroban's interpretation is correct (paretheses needed in the equation), though I can see how ebaines could interpret the equation the way he did without the parentheses.
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  7. #7
    Forum Admin topsquark's Avatar
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    Re: Important question plzzzzzzz help

    Quote Originally Posted by jpritch422 View Post
    I would say that Soroban's interpretation is correct (paretheses needed in the equation), though I can see how ebaines could interpret the equation the way he did without the parentheses.
    I believe Soroban is right also. Now all we need is the OP's comment about it...

    -Dan
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