a) Provide an example of a positive $a$ such that $\{a\}+\left\{{ }^{1} a\right\}=1$.

b) Can such an $a$ be a rational number?
If $=|n|=1$, that is, when $a= \pm 1$. But in this case $\{a\}+\left\{{ }^{1} / a\right\}=0$. Contradiction.
## Answer

a) For example, $a=2+\sqrt{3}$. b) It cannot.