Giải một số bài tập hệ bất phương trình bậc 2 bằng cách đưa về hệ phương trình

Trong chương trình toán phổ thông (ở lớp 10) học sinh được làm quen với hệ phương trình bậc hai hai ẩn. Nếu ta chịu khó phân loại thì sẽ có các loại sau:

1) Hệ gồm một phương bậc nhất và một phương trình bậc hai.

2) Hệ đối xứng (Đối xứng loại I, loại II).

3) Hệ đẳng cấp.

      Học sinh ít nhiều cũng định hình được cách giải các loại hệ nói trên. Trong các loại hệ nói trên ta thay dấu phương trình (dấu đẳng  thức) bởi dấu bất phương trình (dấu bất đẳng thức), thì việc giải các hệ bất phương tương ứng sẽ gặp không ít khó khăn, đó thường là các bài toán trong các kỳ thi học sinh giỏi. Hơn thế nữa nhiều khi ta còn bắt gặp trong các hệ phương trình, hệ bất phương trình có chứa thêm tham số, bài toán yêu cầu tìm điều kiện của tham số để hệ có nghiệm hoặc hệ có nghiệm duy nhất thì vấn đề lại khó hơn nhiều.   

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