Real numbers a and b are chosen with 1<a<b such that no triangle with positive area has side lengths 1, a, and b or \dfrac{1}{b}, \dfrac{1}{a}, and 1 . What is the smallest possible value of b ?
Answer Choices
A. \dfrac{3+\sqrt{3}}{2}
B. \dfrac{5}{2}
C. \dfrac{3+\sqrt{5}}{2}
D. \dfrac{3+\sqrt{6}}{2}
E. 3