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If x+1/x=5 find the value of x^3+1/(x^3)...

If `x+1/x=5` find the value of `x^3+1/(x^3)`

Text Solution

Verified by Experts

Given:
`x+1/x=5`
On Cubing both sides, we get
`x^(3)+1/x^(3) + 3 xx x xx 1/x (x+1/x) = 125`
`(a+b)^(3)=a^(3)+b^(3)+3ab(a+b)`
`=> x^(3)+1/x^(3) +3 xx 5 =125`
`x^(3)+1/x^(3)+ 15=125`
`=>x^(3)+1/x^(3) + 15=125`
`=>x^(3)+1/x^(3)=125-15`
`=110`
Hence the value is`110`
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