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If the value ofA 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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Solution :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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