1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Prove that c=45 or 135

  1. Jan 19, 2013 #1


    User Avatar
    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} \\
    Last edited: Jan 19, 2013
  2. jcsd
  3. Jan 19, 2013 #2


    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


    User Avatar
    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


    User Avatar
    Gold Member

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook