Question 92
Consider two sets $A$ and $B$ of real numbers that have the following properties:
a. $0 \in A$;
b. if $1+x \in A$, then $\sqrt{1+x+x^2} \in B$;
c. if $\sqrt{x^2 - x + 1} \in B$, then $2+x \in A$.
Prove that $\sqrt{3}$, $\sqrt{13}$, $\sqrt{31}$ are elements of the set $B$ and $2024 \in A$.
a. $0 \in A$;
b. if $1+x \in A$, then $\sqrt{1+x+x^2} \in B$;
c. if $\sqrt{x^2 - x + 1} \in B$, then $2+x \in A$.
Prove that $\sqrt{3}$, $\sqrt{13}$, $\sqrt{31}$ are elements of the set $B$ and $2024 \in A$.