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Algebra problem

  1. Jun 4, 2009 #1
    1. The problem statement, all variables and given/known data

    can someone please tell me why maple says that x=root(x^2+1)/x=.5root(2+root(20))??

    ive tried trig and rearranging, but i have idea why this is so..
     
  2. jcsd
  3. Jun 4, 2009 #2

    danago

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    Gold Member

    Have you got a value stored into the variable x?

    EDIT: Oh i think i may have misinterpreted the problem.

    Heres some working:
    http://img4.imageshack.us/img4/8552/algebra.gif [Broken]

    Probably is a quicker way, but these are the steps i took.
     
    Last edited by a moderator: May 4, 2017
  4. Jun 4, 2009 #3

    sylas

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    Science Advisor

    Square both sides, and you get a quadratic in x2. Solve.

    [tex]\begin{align*}
    x &= \frac{\sqrt{x^2+1}}{x} \\
    \intertext{Hence}
    x^2 &= \sqrt{x^2 + 1} \\
    x^4 &= x^2 + 1 \\
    x^2 &= \frac{1 \pm \sqrt{5}}{2} \\
    \intertext{(Must be positive, so dismiss the negative part)}
    & = \frac{2 + \sqrt{20}}{4} \\
    \intertext{Hence}
    x & = \pm 0.5 \sqrt{2 + \sqrt{20}} \\
    &= \pm \sqrt{0.5 + \sqrt{1.25}}
    \end{align*}[/tex]​
     
  5. Jun 4, 2009 #4
    thankyou very much, im still unsure how you get from x^4 to x^2=2+root(20)/4.. but i know its right so thx
     
  6. Jun 4, 2009 #5

    Cyosis

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    Homework Helper

    He uses a substitution p=x^2 and then solves p with the ABC formula.
     
  7. Jun 4, 2009 #6
    ok yes thankyou
     
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