Question

If in a triangle ABC , a^4+b^4+c^4=2c^2(a^2+b^2), prove that C= 45 degree or 135 degree

Answer 1

=>a^4+b^4+c^4=2c^2(a^2+b^2)
=>(a^2+b^2)^2-2a^2.b^2+c^2=2c^2 (a^2+b^2)
=>(a^2+b^2)^2+c^2-2c^2 (a^2+b^2)=2a^2b^2
=>{a^2+b^2-c^2}^2=2a^2b^2
now both side take square root
=>a^2+b^2-c^2=+_root2ab
=> (a^2+b^2-c^2)/2ab =+_1/root2
but we know a/c properties of triangle
LHS is equal to cosC
so, cosC=+_1/root2
hence C=45 degree, 135 degree