JOHN
Lv 7
JOHN asked in Science & MathematicsMathematics · 5 years ago

You are given that a, b, c are the sides of a Δ. Prove that a/(b + c -a) + b/(a +c - b) + c/(a + b - c) ≥ 3.?

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  • 5 years ago
    Favourite answer

    Here:

    Attachment image
    Source(s): I found this one: https://vn.answers.yahoo.com/question/index?qid=20... Although this work contains Vietnamese language, i will try my best to translate it into English and clarify this work.
  • JOHN
    Lv 7
    5 years ago

    Line 2: you've cleared fractions on the LHS, but what did you do on the RHS? It isn't AM-GM, at any rate this isn't applied correctly if it is what you intended. Your line 3 is even more mysterious.

  • 5 years ago

    a/(b + c - a) + b/(a + c - b) + c/(a + b -c) >= 3

    a(a +c - b)(a + b -c) + b(b +c -a)(b + a -c) + c(c +a -b)(c + b - a) >= 3(a +b -c)(b +c -a)(a + c - b)

    a^3 - ab^2 - ac^2 +2abc + b^3 - a^2b - bc^2 + 2abc + c^3 -

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