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Question
If x = `(4 - sqrt(15))`, find the values of
`x^2 + (1)/x^2`
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Solution
`x^2 + (1)/x^2`
`(x^2 + (1)/x^2) = (x + (1)/x)^2 -2` ----(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^2 + (1)/x^2) = (x + (1)/x)^2 -2`
= 82 - 2
= 64 - 2
= 62
`(x^2 + (1)/x^2)` = 62
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