(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

(!) Determine the set of ordered pairs (x,y) of nonzero real numbers such that x/y + y/x >= 2.

2. Relevant equations

x/y + y/x >= 2

3. The attempt at a solution

Relatively new to set notation and proving so, I merely am seeking reassurances that what I am doing is correct.

x/y + y/x >= 2

*Made everything a common denominator*

x^2/xy + y^2/xy >=2xy/xy

(x^2+y^2-2xy)/(xy) >= 0

(x-y)^2/(xy)>=0

(x-y)^2 >= 0

x-y >= 0

x >= y

Set would be written therefore as:

[tex]\left\{\left(x,y\right) \in\Re: x \geq y\right\}[/tex]

But x and y cannot equal zero (not sure how to depict that in set notation).

Sincerely,

NastyAccident

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# Homework Help: Set of Ordered pairs question

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