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Question

If a, b, c are three positive real number then show : ab+c+ba+c+ca+b32

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Solution

ab+c+ba+c+ca+b33b+ca+a+cb+a+bc (AM>HM)
ab+c+ba+c+ca+b33ba+ab+ca+ac+cb+bc
ab+c+ba+c+ca+b336(ab+ba2)(AM>GM)
ab+c+ba+c+ca+b32

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