Its a bit cleaner if you substitute x = sqrt(2) + sqrt(3) in first.Then combine the two fractions:(sqrt(6) (sqrt(5) - x) + sqrt(6) (sqrt(5) + x)) / 5 - x^2= 2 sqrt(30) / 5 - x^2x^2 = (5 + 2 sqrt(6))Then subsituting that back in you get 2 sqrt(30) / - 2 sqrt(6) = - sqrt(5)
Thank you so much Benjamin Leis
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2 comments:
Its a bit cleaner if you substitute x = sqrt(2) + sqrt(3) in first.
Then combine the two fractions:
(sqrt(6) (sqrt(5) - x) + sqrt(6) (sqrt(5) + x)) / 5 - x^2
= 2 sqrt(30) / 5 - x^2
x^2 = (5 + 2 sqrt(6))
Then subsituting that back in you get
2 sqrt(30) / - 2 sqrt(6)
= - sqrt(5)
Thank you so much Benjamin Leis
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