Irska

Question

Suppose a, b, c are the side lengths of a triangle. Prove that a1+a, b1+b, c1+c are also the side lengths of a triangle.

Accepted Answer

First of all, if x, y > -1, then x1+x < y1+y x+xy < y+yx, i.e., iff -1 < x < y. Hence, since a < b + c, and b, c > 0, a1+a < b+c1+b+c = b1+b+c + c1+b+c < b1+b + c1+c, as required.