Question 148
Let $n \ge 3$ be an integer and $A$ be a set with $n$ elements so that, for every $a, b \in A, a \neq b$, the number $a^2 + b\sqrt{3}$ is rational.
a) Give an example of such a set $A$.
b) Prove that, if $x \in A$, then $x\sqrt{3}$ is rational.
a) Give an example of such a set $A$.
b) Prove that, if $x \in A$, then $x\sqrt{3}$ is rational.