# Prove that c=45 or 135

1. Jan 19, 2013

### utkarshakash

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

2. Relevant equations

3. The attempt at a solution
Rearranging I have

$(a^c-c^2)^2+b^2(b^2-2c^2)=0 \\ cos C=\dfrac{a^2+b^2-c^2}{2ab} \\ a^2-c^2=2abcosC-b^2$

Last edited: Jan 19, 2013
2. Jan 19, 2013

### 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.

3. Jan 19, 2013

### utkarshakash

I have edited the question. Please see again.

4. Jan 19, 2013

### Saitama

Start by investigating the expansion of $(a^2+b^2-c^2)^2$. Its pretty straightforward after that.

5. Jan 20, 2013

Thanks