11th Class Mathematics Other Series Question Bank Critical Thinking

  • question_answer If \[a,\ b,\ c\] are the positive integers, then \[(a+b)(b+c)(c+a)\]is [DCE 2000]

    A) \[<8abc\]

    B) \[>8abc\]

    C) \[=8abc\]

    D) None of these

    Correct Answer: B

    Solution :

    Since A.M. > G.M.,  we have \[\frac{a+b}{2}>\sqrt{ab},\ \frac{b+c}{2}>\sqrt{bc}\] and \[\frac{a+c}{2}>\sqrt{ac}\]. Multiplying these inequalities, we get \[(a+b)(b+c)(c+a)>8abc\].


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