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Question
If x = `(4 - sqrt(15))`, find the values of
`x^3 + (1)/x^3`
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Solution
`x^3 + (1)/x^3`
`(x^3 + (1)/x^3) = (x + (1)/x)^3 -3(x + (1)/x)` -----(1)
we will first find the value of `x + (1)/x`
`x + (1)/x = (4 - sqrt(15)) + (1)/((4 - sqrt(15))`
= `((4 - sqrt(15))^2 + 1)/((4 - sqrt(15))`
= `(16 + 15 - 8sqrt(15) + 1)/((4 - sqrt(15))`
= `(8(4 - sqrt(15)))/((4 - sqrt(15))`
= 8
substituting the valuesin (1)
`(x^3 + (1)/x^3) = (x + (1)/x)^3 -3(x + (1)/x)`
= 83 - 24
= 488
`(x^3 + (1)/x^3)` = 488
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