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Question
If x = `(7 + 4sqrt(3))`, find the values of :
`(x + (1)/x)^2`
Solution
x = `7 + 4sqrt(3)`
∴ `(1)/x = (1)/(7 + 4sqrt(3))`
= `(1)/(7 + 4sqrt(3)) xx (7 - 4sqrt(3))/(7 - 4sqrt(3))`
= `(7 - 4sqrt(3))/(7^2 - (4sqrt(3))^2`
= `(7 - 4sqrt(3))/(49 - 48)`
= `(7 - 4sqrt(3))/(1)`
= `7 - 4sqrt(3)`
∴ `x + (1)/x `
= `(7 + 4sqrt(3)) + (7 - 4sqrt(3))`
= `7 + 4sqrt(3) + 7 - 4sqrt(3)`
= 14
Hence, `(x + (1)/x)^2`
= (14)2
= 196
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