Question
If `x = (sqrt(3) + 1)/(sqrt(3) - 1)` and ` y = (sqrt(3) - 1)/(sqrt(3) + 1)` then the value of `(x^2 + y^2)` is
Answer: Option C
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`x` = `((sqrt(3) + 1))/((sqrt(3) - 1)) xx ((sqrt(3) + 1))/((sqrt(3) +1)) ` = `((sqrt(3) + 1)^2)/((3 - 1 ))`
= `(3 + 1 + 2sqrt(3))/(2)` = 2 + `sqrt(3)`
y = `((sqrt(3) - 1))/((sqrt(3)+1)) xx ((sqrt(3) -1))/((sqrt(3)-1)) ` = `((sqrt(3) - 1)^2)/((3 - 1))`
= `(3 + 1 - 2sqrt(3))/(2)` = `2 - sqrt(3)`
`:.` `x^2 + y^2` = ` (2 + sqrt(3))^2 + (2 - sqrt(3))^2` = 2(4 + 3) = 14.
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