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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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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`
Posted by justaguide on June 20, 2013 at 5:52 AM (Answer #1)
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