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Nội dung: <blockquote data-quote="hoaluuly92" data-source="post: 50941" data-attributes="member: 75385">Cho <img src="https://www.psit.in/cgi-bin/mimetex.cgi?%5Clarge%20a,b,c" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />là các số thực dương. Khi đó với mọi <img src="https://www.psit.in/cgi-bin/mimetex.cgi?%5Clarge%20r%5Cge%200" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />th“ <img src="https://www.psit.in/cgi-bin/mimetex.cgi?%5Clarge%20%5Cfbox%7Ba%5Er%28a-b%29%28a-c%29+b%5Er%28b-c%29%28b-a%29+c%5Er%28c-a%29%28c-b%29%5Cge%200%7D" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />dấu bằng xảy ra khi và chỉ khi <img src="https://www.psit.in/cgi-bin/mimetex.cgi?%5Clarge%20a=b=c" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />hoặc <img src="https://www.psit.in/cgi-bin/mimetex.cgi?%5Clarge%20a=b" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />và <img src="https://www.psit.in/cgi-bin/mimetex.cgi?%5Clarge%20c=0" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />cùng các hoán vị của nó.Chứng minh:Không mất tính tổng quát ta có thể giả sử <img src="https://www.psit.in/cgi-bin/mimetex.cgi?%5Clarge%20a%5Cge%20b%5Cge%20c" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Ta có :<img src="https://www.psit.in/cgi-bin/mimetex.cgi?%5Clarge%20a%5Er%28a-b%29%28a-c%29+b%5Er%28b-c%29%28b-a%29+c%5Er%28c-a%29%28c-b%29%5Cge%200" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://www.psit.in/cgi-bin/mimetex.cgi?%5Clarge%20%5CLeftrightarrow%20%5Csum%20a%5Er%20[%28a-b%29%5E2+%28a-c%29%5E2-%28b-c%29%5E2%20]%5Cge%200%5C%5C%20%5CLeftrightarrow%20%5Csum%20%28b-c%29%5E2%28c%5Er+b%5Er-%20a%5Er%29%5Cge%200" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Bất đẳng thức đã qui về dạng chính tắc với:<img src="https://www.psit.in/cgi-bin/mimetex.cgi?%5Clarge%20S_a=c%5Er+b%5Er-a%5Er%20%5C%5C%20S_b=a%5Er+c%5Er-b%5Er%20%5C%5C%20S_c=a%5Er+b%5Er-c%5Er" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Dễ thấy ta có <img src="https://www.psit.in/cgi-bin/mimetex.cgi?%5Clarge%20S_b,%20S_c%5Cge%200" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Ta cần chứng minh <img src="https://www.psit.in/cgi-bin/mimetex.cgi?%5Clarge%20S_c+S_a%5Cge%200" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Thật vậy ta có <img src="https://www.psit.in/cgi-bin/mimetex.cgi?%5Clarge%20S_c+S_a=2b%5Er%5Cge%200" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />. Dấu bằng xảy ra khi và chỉ khi <img src="https://www.psit.in/cgi-bin/mimetex.cgi?%5Clarge%20a=b=c" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />hoặc<img src="https://www.psit.in/cgi-bin/mimetex.cgi?%5Clarge%20%20a=b" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />và <img src="https://www.psit.in/cgi-bin/mimetex.cgi?%5Clarge%20c=0" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />cùng các hoán vị của nó.</blockquote>

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