InterviewSolution
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InterviewSolution
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The number of integers satisfying `log_((1)/(x))((2(x-2))/((x+1)(x-5)))ge 1` is |
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Answer» Correct Answer - A Case I: `1//x gt 1` or `0 lt x lt 1` `therefore log_((1)/(x))((2(x-2))/((x+1)(x-5)))ge 1` `rArr (2(x-2))/((x+1)(x-5))ge(1)/(x)` `rArr (2(x-2))/((x+1)(x-5))-(1)/(x)ge0` `rArr (2x(x-2)-(x+1)(x-5))/(x(x+1)(x-5))ge0` `rArr (x^(2)+5)/(x(x+1)(x-5))ge 0` `rArr x in (-1,0) uu (5, oo)` Hence, no solution in this case. Case II : `0 lt (1)/(x)lt 1` or `x gt 1` `therefore 0 lt x lt 5` Also `(2(x-2))/((x+1)(x-5))gt 0` `therefore x in (1,2)` |
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