1.
[tex] \dfrac{x}{y}+\dfrac{y}{x} > 2|\cdot xy\\
x^2+y^2>2xy\\
x^2-2xy+y^2>0\\
(x-y)^2>0 [/tex]
[tex] (x-y)^2>0 [/tex] is true for any two real numbers such that [tex] x\not =y [/tex], all the more for positive ones.
2.
[tex] x=y [/tex]
The (x/y) + (y/x) > 2 is always correct for real numbers except x = y then inequality becomes an equality.
The number system is a way to represent or express numbers.
All number that we can think of is a real number except complex numbers.
The Number System includes any of the several sets of symbols and the rules for using them to represent numbers.
A decimal number is a very common number that we use frequently.
Given two real numbers x and y
(x/y) + (y/x) > 2
Taking LCM
(x² + y²)/xy > 2
x² + y² > 2xy
x² + y² - 2xy > 0
(x - y)² > 0
This is always correct for two real numbers except x = y at this condition x - y = 0 and 0 = 0 so inequality converts into equality.
Hence, the (x/y) + (y/x) > 2 is always correct for real numbers except x = y then inequality becomes an equality.
For more about the number system,
https://brainly.com/question/22046046
#SPJ2
