Let \(a,b,c>0\) be the length of sides of a triangle. Show that the triangle is right-angled if and only if \((a^4+b^4+c^4)^2 = 2(a^8+b^8+c^8)\). Note that this is a symmetric characterization of right-angled triangles by its side lengths.
Let \(a,b,c\) be numbers. If \(a+b=c\), show that \(a=c-b\).