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Prove that c=45 or 135

  1. Jan 19, 2013 #1

    utkarshakash

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    Gold Member

    1. The problem statement, all variables and given/known data
    If in a triangle ABC, [itex]a^4+b^4+c^4=2c^2(a^2+b^2)[/itex], prove that c=45° or 135°

    2. Relevant equations

    3. The attempt at a solution
    Rearranging I have

    [itex](a^c-c^2)^2+b^2(b^2-2c^2)=0 \\

    cos C=\dfrac{a^2+b^2-c^2}{2ab} \\
    a^2-c^2=2abcosC-b^2[/itex]
     
    Last edited: Jan 19, 2013
  2. jcsd
  3. Jan 19, 2013 #2

    Mark44

    Staff: Mentor

    You have things tangled up here, I believe. The lowercase letters a, b, and c typically represent the lengths of the sides. The uppercase letters A, B, and C typically represent the angle measures. Angle C would be the angle across from the side of length c. It's confusing to me that you use c for what appears to be a side length and an angle.


     
  4. Jan 19, 2013 #3

    utkarshakash

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    Gold Member

    I have edited the question. Please see again.
     
  5. Jan 19, 2013 #4
    Start by investigating the expansion of ##(a^2+b^2-c^2)^2##. Its pretty straightforward after that.
     
  6. Jan 20, 2013 #5

    utkarshakash

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    Gold Member

    Thanks
     
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