SOLUTION: {{{x=(3 + sqrt ( 5 ))/(3 - sqrt ( 5 ))}}} and {{{y =(3 - sqrt ( 5 ))/(3 + sqrt ( 5 ))}}}. calculate {{{x^3 + y^3}}}
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Question 762576: and . calculate
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
This a lot of multiplying, but here goes. Start with
(1)
Now multiply numerator and denominator of (1) by
(2) and get
(3) or
(4) or
(5)
Now get
(6) or
(7)
Now get from
(8) or
(9) or
(10) or
(11) or
(12)
From the original problem we see that
(13) y = 1/x or
(14) or
(15)
Now add (12) and (15) to get the desired sum
(16) or
(17) or
(18)
The GCF of the numerator of (18) is 2*7*23 or 322. So we can write (18) as
(19) which reduces to
the final answer,
(20)
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