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# How solve equation `1/sqrt(x) +1/sqrt y=1/sqrt(20)` for natural numbers x and y

user123454321876 | eNotes Newbie

Posted June 19, 2013 at 6:02 PM via web

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How solve equation `1/sqrt(x) +1/sqrt y=1/sqrt(20)` for natural numbers x and y

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### 1 Answer |

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 20, 2013 at 5:52 AM (Answer #1)

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The equation `1/sqrt x + 1/sqrt y = 1/sqrt 20` has to be solved where x and y are natural numbers.

`1/sqrt x + 1/sqrt y = 1/sqrt 20`

=> `(sqrt y + sqrt x)/(sqrt(x*y)) = sqrt 20/20`

`sqrt(x*y) = 20 and sqrt x + sqrt y = sqrt 20`

=> `x*y = 400` and `x + y + 2*sqrt(x*y) = 20`

`x + y + 2*sqrt(x*y) = 20`

=> `x + y + 40 = 20`

=> `x + y = -20`

But natural numbers refers to the set of non-negative numbers.

There is no natural number solution for `1/sqrt x + 1/sqrt y = 1/sqrt 20`

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