SOLUTION: [(sqrt(3+sqrt5)) - (sqrt(3-sqrt5))]^2 = 2
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Question 1117380: [(sqrt(3+sqrt5)) - (sqrt(3-sqrt5))]^2 = 2
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
[(sqrt(3+sqrt5)) - (sqrt(3-sqrt5))]^2 = 2
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Take the sqrt of both sides to get:
sqrt(3+sqrt(5)) - sqrt(3-sqrt(5)) = sqrt(2)
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2.2882 - 0.874 = 1.414
1.414 = 1.414
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Cheers,
Stan H.
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Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
^2\ =^? \ 2)
Expand the binomial in the LHS
\ -\ 2\(\sqrt{3\ +\ \sqrt{5}}\)\(\sqrt{3\ -\ \sqrt{5}}\)\ +\ \(3\ -\ \sqrt{5}\)\ =^?\ 2)
Collect like terms and calculate the product of conjugates in the center term of the LHS
\ =^?\ 2)
\ \equiv\ 2)
John
My calculator said it, I believe it, that settles it
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