Let the sides of the triangle be a=13,b=7 and c=8.
Since a is the longest side the greatest angle is A.
Using Cosine rule, we have
when k=1 we have
But we have in a triangle the sum of the three angles is 180 degrees ,so if B=90 degrees then
In a (b +c) cos A + (c + a) cos B + (a + b) cos C is equal to
Hence c is the root of the equation