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(x+(1)/(x))^(6)...

`(x+(1)/(x))^(6)`

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`(x +(1)/(x))^(6)=^(6)C_(0)x^(6)((1)/(x))^(0)+^(6)C_(1)x^(5)((1)/(x))^(1)`
`+^(6)C_(2)x^(4)((1)/(x))^(2)+^(5)C_(3) x^(3)((1)/(xx))^(3)+^(6)C_(4)x^(2)((1)/(x))^(4)`
`+^(6)C_(5)x((1)/(x))^(5)+^(6)C_(6)x^(0)((1)/(x))^(6)`
`=^(6)C_(0).x^(6)+^(6)C_(1).x^(4)+^(6)C_(2).x^(2)+^(6)C_(3).1`
`+^(6)C_(4).(1)/(x^(2))+^(6)C_(5).(1)/(x^(4))+^(6)C_(6).(1)/(x^(6))`
`=1.x^(6)+(6)/(1).x^(4)+(6xx5)/(2xx1)x^(2)+(6xx5xx4)/(3xx2xx1)`
`+(6xx5)/(2xx1)(1)/(x^(2))+(6)/(1).(1)/(x^(4))+1.(1)/(x^(6))`
`=x^(6)+6x^(4)+15x^(2)+20+(15)/(x^(2))+(6)/(x^(4))+(1)/(x^(6))`
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