Phương trình `1:`

`x_{1} + x_{2} = -2023, x_{1} * x_{2} = 2`

Phương trình 2:

`x_{3} + x_{4} = -2024, x_{3} * x_{4} = 2`

Tính:

`A = (x_{1} + x_{3})(x_{2} - x_{3})(x_{1} + x_{4})(x_{2} - x_{4})`

`= (x_{1} + x_{3})(x_{1} + x_{4})(x_{2} - x_{3})(x_{2} - x_{4})`

Tính từng phần:

`(x_{1} + x_{3})(x_{1} + x_{4}) = x_{1}^{2} + x_{1}(x_{3} + x_{4}) + x_{3} * x_{4}`

`= x_{1}^{2} + x_{1}(-2024) + 2`

`(x_{2} - x_{3})(x_{2} - x_{4}) = x_{2}^{2} - x_{2}(x_{3} + x_{4}) + x_{3} * x_{4}`

`= x_{2}^{2} + 2024x_{2} + 2`

Thay `x_{1}^{2} = -2023x_{1} - 2:`

`x_{1}^{2} - 2024x_{1} + 2 = (-2023x_{1} - 2) - 2024x_{1} + 2 = -4047x_{1}`

Thay `x_{2}^{2} = -2023x_{2} - 2:`

`x_{2}^{2} + 2024x_{2} + 2 = (-2023x_{2} - 2) + 2024x_{2} + 2 = x_{2}`

Vậy:

`A = (-4047x_{1})·x_{2} = -4047(x_{1}·x_{2}) = -4047 xx 2 = -8094`

`@#Yuirii`