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Question
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of
x2 + y2
Solution
x2 + y2
x2 + y2 = (x + y)2 - 2xy ----(1)
∴ (x + y) = `((sqrt(3) + 1))/((sqrt(3) - 1)) + ((sqrt(3) - 1))/((sqrt(3) - 1)`
= `((sqrt(3) + 1)^2 + (sqrt(3) - 1)^2)/(3 - 1)`
= `(3 + 1 + 2sqrt(3) + 3 + 1 - 2sqrt(3))/(2)`
= `(8)/(2)`
= 4
and xy = `((sqrt(3) + 1))/((sqrt(3) - 1)) xx ((sqrt(3) - 1))/((sqrt(3) + 1)`
= 1
substituting in (1), we get
x2 + y2
= (x + y)2 - 2xy
= 16 - 2
= 14
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