SOLUTION: Show that [ sqrt(3 + sqrt(5)) - sqrt(3 - sqrt(5))]^2 = 2

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Question 1117328: Show that [ sqrt(3 + sqrt(5)) - sqrt(3 - sqrt(5))]^2 = 2
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
To ease the notation, let A = +sqrt%283+%2B+sqrt%285%29%29+ and B = +sqrt%283+-+sqrt%285%29%29+
Then the Left Hand Side is +%28A+-+B%29+%5E2+
+%28A-B%29%5E2++=+A%5E2+-+2AB+%2B+B%5E2++=+%28A%5E2%2BB%5E2%29+-+2AB+
+A%5E2+=++3+%2B+sqrt%285%29+
+B%5E2+=+3+-+sqrt%285%29+
+A%5E2+%2B+B%5E2++=++6+

so +%28A%5E2%2BB%5E2%29+-2AB+=+6-4+=+2+ Done.