Ta có: (x-2022)^2 + (x-2024)^2 >= 2
<=> (x-2022)^2 + (x-2024)^2 - 2 >= 0
<=> (x-2022)^2 + (x-2024)^2 -1 -1 >= 0
<=> [(x-2022)^2 -1]+ [(x-2024)^2-1] >= 0
<=> (x-2022 + 1) (x-2022-1) + (x-2024+1) (x-2024-1) >= 0
<=> (x-2021) (x-2023) + (x-2023) (x-2025) >= 0
<=> (x-2023) (x-2021+x-2025) >= 0
<=> (x-2023) (2x -4046) >=0
<=> (x-2023) 2(x-2023) >= 0
<=> 2(x-2023)^2 >=0
Ta có: 2(x-2023)^2 >=0 với mọi x
Vậy (x-2022)^2 + (x-2024)^2 >=2