MIE 2015/Day 1/Problem 6
Let be a geometric progression and be an arithmetic progression, both in these order, so we can say that , and :
(a) are the sides of an obtusangle triangle.
(b) are the sides of an acutangle triangle that's not equilateral.
(c) are the sides of an equilateral triangle.
(d) are the sides of a right triangle.
(e) can't be the sides of a triangle.
So we got these three relations
By these equations we can see that , so it can't be an equilateral triangle.
First, we must see if , and are the sides of a tringle.
So, , and can't be the sides of a triangle.