Let x and y be two irrational numbers Prove that at least on

Let x and y be two irrational numbers. Prove that at least one of x+y or x-y has to be irrational as well.

Solution

X and y are two irrational no.s then x+y or x-y atleast one should be irrational,

Say both x+y as well as x-y are rational, but if x+y is rational then irrational part of x or y are cancel out i. e one of them are opposite sign of other, hence for x-y it will get added and makes x-y irrational, and vice versa.