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If the value of `A` for which the equation `cot^(3)A+cot^(2)A|cotA+x|+|cot^(2) Ax+1|=1` has not less than 6 different solutions which are integers are `[cot^(-1)alpha, pi)uu[cot^(-1)beta,cot^(-1)gamma]` then |
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Answer» Correct Answer - 4 Let `cotA=a` then `a^(3)+a^(2)|a+x|+|a^(2)x+1|=1` `|a^(3)+a^(2)x|+|a^(2)x+1|=(a^(2)+1)-(a^(2)x+a^(3))` `|alpha|+|beta|=alpha=beta` So, `alpha ge 0` and `beta le0` Now take cases: `a le -1`and `-1 lt le 0` & `0lt ale 1` Finally we get `aepsilon (-oo,-5]uu[1/(sqrt(5)),1/(sqrt(6))]` |
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