Sunday, October 5, 2008

Problem Of The Week 44

FInd the number of pairs (x,y) of integers 0<x<y such that sqrt(x)+sqrt(y)=sqrt(1984)

8 comments:

  1. 991 pairs
    1,(1983)^2 to (991)^2,(993)^2

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  2. pairs can be [1,1983], [2,1982].....[1984,1]. {for sqrt {x} and sqrt{y}}
    but y>x, so, sqrt{y}>sqrt{x}. so, pairs are till before{991,991}
    hence, there are 990 pairs for root{y} and root{x} . and there fore for x and y too.

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  3. sorry there was an error in question
    kindly try again !

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  4. (1,7) (2,6) (3,5)
    each number in each pair multiplied by sqrt(31)

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  5. yaar, we have to give (x,y) pairs. so there are 6 pairs.
    3 others are (7,1) ,(6,2) , (5,3). correct me if i am wrong.

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  6. no the answer would still be three because x must be less than y

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