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Digit Hunting (Posted on 2019-01-26) Difficulty: 3 of 5
Find the third digit after the decimal point of

(2 + √5)100((1 + √2)100 + (1 + √2)-100)

No Solution Yet Submitted by Danish Ahmed Khan    
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re: poor explanation | Comment 3 of 4 |
(In reply to poor explanation by Jer)

Maybe adding a term will help.  Make the expression [(2 + √5)^100 + (2 - √5)^100] * [(1 + √2)^100 + (1 + √2)^-100] and see how much the (2-√5) affects the result.


You already noted the relation between 1+√2 and 1-√2.  Now do that to 2+√5 and 2-√5.  Also, 1-√2 and 2-√5 have an absolute value less than 1.

  Posted by Brian Smith on 2019-01-27 12:18:03
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