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Question
If `3"x"+1/(3"x")=3`, find : `27"x"^3+1/(27"x"^3)`
Sum
Solution
`3"x"+1/"3x"=3`
`⇒(3"x"+1/"3x")^3=(3)^3`
`⇒(3"x")^3+(1/"3x")^3+3xx3"x"xx1/"3x"(3"x"+1/"3x")=27`
`⇒27"x"^3+1/"27x"^3+3(3"x"+1/"3x")=27`
`⇒27"x"^3+1/"27x"^3+3(3)=27`
`⇒27"x"^3+1/"27x"^3+9=27`
`⇒27"x"^3+1/"27x"^3=27-9`
`⇒27"x"^3+1/"27x"^3=18`
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