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If x-1/x=7 find the value of x^3-1/(x^3)...

If `x-1/x=7` find the value of `x^3-1/(x^3)`

Text Solution

Verified by Experts

Using identity
`(a-b)^(3)=a^(3)-b^(3)+3ab(a-b)`
`(x-1/(x^3))^(3)=x^3-1/(x^3) - 3 xx x xx 1/x(1/x -x)`
`(x-1/(x^3))^(3)=x^3-1/(x^3) - 3(1/x -x)`
`=7^(3)=x^3-1/(x^3) - 3(7)`
`x^3-1/(x^3)=7^(3) + 21`
`=49 xx 7 + 21`
`=343 + 21`
`=364`
Hence the value of `x^3-1/(x^3)` is`364`
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