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JEE Main & Advanced Sample Paper JEE Main Sample Paper-42

  • question_answer
    If a, b and c are distinct positive numbers, then the expression (b + c - a) (a + c - b) (a +b - c) - abc is

    A)  positive                      

    B)  negative

    C)  non-positive   

    D)  non-negative

    Correct Answer: B

    Solution :

    Since,\[AM>GM\] \[\therefore \]\[\frac{(b+c-a)+(c+a-b)}{2}\] \[>{{[b+c-a(c+a-b)]}^{1/2}}\] \[\Rightarrow \]\[c>{{[b+c-a(c+a-b)]}^{1/2}}\]                ?(i) Similarly. \[b>[{{(a+b-c(b+c-a)]}^{1/2}}\]               ?(ii) and\[a>{{[(a+b-c)(c+a-b)]}^{1/2}}\]                    ?(iii) On multiplying Eqs. (i), (ii) and (iii), we get \[abc>(a+b-c)(b+c-a)(c+a-b)\]Hence, \[(a+b-c)(b+c-a)(c+a-b)-abc<0\]


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