Re: Rational and irrational numbers
- From: quasi <quasi@xxxxxxxx>
- Date: Sun, 28 Aug 2005 09:37:24 -0700
On 28 Aug 2005 06:01:06 -0700, deepkdeb@xxxxxxxxx wrote:
>I would appreciate any comment upon the correctness of the following
>assertion:
>
>Consider (1) below
>xy = z (1) where x,y,z are real numbers such that z is an
>integer,both x and y are irrational.
>Assertion: Both x and y must satisfy (2) and (3); (a,b) = 1.
>x = sqrt(a)+ sqrt(b) (2) and y = sqrt(a) - sqrt(b) (3)
>where atleast one of a or b must be a non-square.
Incorrect.
If z is a given integer, then you can choose any nonzero real number
for x and simply let y=z/x.
quasi
.
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