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Question
If x = `(4 - sqrt(15))`, find the values of:
`(x + (1)/x)^2`
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Solution
x = `4 - sqrt(15)`
∴ `(1)/x = (1)/(4 - sqrt(15))`
= `(1)/(4 - sqrt(15)) xx (4 + sqrt(15))/(4 + sqrt(15))`
= `(4 + sqrt(15))/(4^2 - (sqrt(15))^2`
= `(4 + sqrt(15))/(16 - 15)`
= `(4 + sqrt(15))/(1)`
= `4 + sqrt(15)`
∴ `x + (1)/x = (4 - sqrt(15)) + (4 + sqrt(15))`
= `4 - sqrt(15) + 4 + sqrt(15)`
= 8
Hence, `(x + (1)/x)^2`
= (8)2
= 64
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