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Question
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x3 + y3
Solution
x3 + y3
(x3 + y3) = (x + y)3 - 3xy (x + y) ----(1)
Now, x + y = `(1)/((3 - 2sqrt(2))) + (1)/((3 + 2sqrt(2))`
= `((3 + 2sqrt(2)) + (3 - 2sqrt(2)))/((3 - 2sqrt(2))(3 + 2sqrt(2))`
= `(6)/(9 - 8)`
= 6
and xy = `(1)/((3 - 2sqrt(2))) xx (1)/((3 + 2sqrt(2))`
= `(1)/(9 - 8)`
= 1
substituting the valuesin (1), we get
(x3 + y3)
= (x + y)3 - 3xy (x + y)
= 216 - 3 x 6
= 198
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