Let $a \geq b \geq c > 0$ be real numbers such that for all $n \in \mathbb { N }$, there exist triangles of side lengths $a ^ { n } , b ^ { n } , c ^ { n }$. Prove that the triangles are isosceles.
Let $a \geq b \geq c > 0$ be real numbers such that for all $n \in \mathbb { N }$, there exist triangles of side lengths $a ^ { n } , b ^ { n } , c ^ { n }$. Prove that the triangles are isosceles.