Question

In a triangle abc,if a^4+ ^4+c^4=2c^2(a^2+b^2),then angle c is equal to

Answer 1

=a4+b4+c4=2c2(a2+b2)

=a+b+c-2ac-2bc=0

add 2ab on both sides,we get

=a+b+c+2ab-2bc-2ca=2ab,

=(a+b-c)=2ab

multiply and divide with 2 on RHS of the equation.we get \frac{(a^{2}+b^{2}-c^{2})^{2}}{4b^{2}c^{2}}

=\frac{1}{2},

we know that cosC=\frac{a^{2}+b^{2}-c^{2}}{2bc},

cos2C=\frac{1}{2}

cosC=\frac{1}{\sqrt{2}},

we get C=\frac{\pi }{4} or \frac{3\pi }{4}

Answer 2

Answer:

it's confusing.It is a useless answer.