cho tam giác abc có a^2019+b^2019=c^2019.Cmr abc là tam giác nhọn
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Đã xảy ra lỗi rồi. Bạn thông cảm vì sai sót này.
Ta có:
Áp dụng hệ quả của bất đẳng thức Cauchy cho ba số không âm
trong đó với
, ta có:
Tương tự, ta có:
Cộng ba bất đẳng thức
và
, ta được:
Khi đó, ta chỉ cần chứng minh
Thật vậy, bất đẳng thức cần chứng minh được quy về dạng sau: (bất đẳng thức Cauchy cho ba số
)
Hay
Mà đã được chứng minh ở câu
nên
luôn đúng với mọi
Dấu xảy ra
Vậy,