Let x and y be rational numbers such that x
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A: Prove or disprove that there exist rational numbers x, y in Q such that √11 = x+y√5.
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Q: Number Theory
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Q: 3. The rational numbers are dense in R. This means that between any two real numbers a and b with a…
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- If x and y are positive rational numbers, prove that there exists a positive integer n such that nxy. This property is called the Archimedean Property of the rational numbers. (Hint: Write x=a/b and y=c/d with each of a,b,c,d+.)Prove that is irrational. (That is, prove there is no rational number such that .)Prove that if is a nonzero rational number and is irrational, then is irrational.