Question 26
Consider a set $M$ of real numbers satisfying the following properties:
a) $(1 + \sqrt{2}) \in M;$
b) if $x, y \in M$, then $x \cdot y \in M$ and $(6x - y) \in M$;
c) if $(6x + y) \in M$, then $x \in M$ or $y \in M$.
Prove that the numbers $3 + 4\sqrt{2}$, $\sqrt{2} - 1$, and $2025$ are elements of the set $M$.
a) $(1 + \sqrt{2}) \in M;$
b) if $x, y \in M$, then $x \cdot y \in M$ and $(6x - y) \in M$;
c) if $(6x + y) \in M$, then $x \in M$ or $y \in M$.
Prove that the numbers $3 + 4\sqrt{2}$, $\sqrt{2} - 1$, and $2025$ are elements of the set $M$.