A1 Let $x$ be a real number such that $(x-2)(x+2)=2021$. Determine the value of $(x-1)(x+1)$.
Solution: Expanding $(x-2)(x+2)=2021$ yields $x^{2}-4=2021$. Hence, $x^{2}=2025$. Therefore, $(x-1)(x+1)=x^{2}-1=2025-1=2024$.
Answer: 2024 .