Based on what we established about the classification of x and using the closure of integers, what does the equation tell you ab

Question

3 years ago

14

Based on what we established about the classification of x and using the closure of integers, what does the equation tell you ab

out the type of number x must be for the sum to be rational? What conclusion can you now make about the result of adding a rational and an irrational number?

Mathematics

2 answers:

Paladinen [302] · Answer 1 · 2022-04-14T13:30:58+03:00

Paladinen [302]3 years ago

6 0

Answer:

Step-by-step explanation:

Hatshy [7] · Answer 2 · 2022-04-14T15:51:53+03:00

Answer: The product of a rational number with an irrational number is an irrational number. To see this assume that x is a rational number and y an irrational number. Then let us assume that the product xy is rational, which means that there are integers a,b such that xy=a/b. But then we obtain y=(1/x)(a/b) which is also rational since the set of rational numbers is closed under multiplication. But this is a contradiction since y was assumed to be an irrational number.