Question

If a, b and c are the sides of a triangle such that $a^4+b^4+c^4=2c^2(a^2+b^2)$ then the angles opposite to the side C is

• A. 45
• B. 120
• C. 135
• D. 150

Answer 1

Answer: (A), (C)

The correct options are
A 45
C 135

$a^4+b^4+c^4-2a^2{c}^2-2b^2{c}^2+2a^2{b}^2=2a^2{b}^2$
$(a^2+b^2-c^2)=(\sqrt{2}ab{)}^2$
$\Rightarrow a^2+b^2-c^2=\pm \sqrt{2}ab$
$\Rightarrow \frac{a^2+b^2-c^2}{2ab}=\pm \frac{\sqrt{2}}{2}$
$\Rightarrow cosC=\pm \frac{1}{\sqrt{2}}\Rightarrow c={45}^{\circ }$ are ${135}^{\circ }$