InterviewSolution
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InterviewSolution
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If a, b and c are distinct positive numbers, then the expression `(a + b - c)(b+ c- a)(c+ a -b)- abc` is:A. positiveB. negativeC. non-positiveD. non-negative |
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Answer» Correct Answer - B Using `A.M.geG.M.,` we have `((b+c-a)+(c+a-b))/(2)gt[(b+c-a)(c+a-b)]^(1//2)` `((c+a-b)+(a+b-c))/(2)gt{(c+a-b)(a+b-c)}^(1//2)` and, `((a+b-c)+(b+c-a))/(2)gt{(a+b-c)(b+c-a)}^(1//2)` `implies" "cgt[(b+c-a)(c+a-b)]^(1//2),age{(c+a-b)(a+b-c)}^(1//2)` and, `bgt{(a+b-c)(b+c-a)}^(1//2)` `implies" "abcgt(a+b-c)(b+c-a)(c+a-b)[{:("On multiplying"),("three inequalities"):}]` `implies" "(a+b-c)(b+c-a)(c+a-b)-abclt0` |
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