Problem: What is the value of
2a−1+a−12a\dfrac{2 a^{-1}+\dfrac{a^{-1}}{2}}{a} a2a−1+2a−1
when a=12a=\dfrac{1}{2}a=21 ?
Answer Choices:
A. 111 B. 222 C. 52\dfrac{5}{2}25 D. 101010 E. 202020 Solution:
2(12)−1+(12)−1212=(2⋅2+22)⋅2=10\dfrac{2\left(\dfrac{1}{2}\right)^{-1}+\dfrac{\left(\dfrac{1}{2}\right)^{-1}}{2}}{\dfrac{1}{2}}=\left(2 \cdot 2+\dfrac{2}{2}\right) \cdot 2= \boxed{10} 212(21)−1+2(21)−1=(2⋅2+22)⋅2=10
The problems on this page are the property of the MAA's American Mathematics Competitions