# Answer to Question #14570 in Real Analysis for bagia artha

Question #14570

Prove that if x is a rational number and y is an irrational number, then x + y is an irrational

number. If, in addition, x is not equal to 1, then show that xy is an irrational number.

number. If, in addition, x is not equal to 1, then show that xy is an irrational number.

Expert's answer

x -rational

y - irrational

If z=x+y rational then y=z-x is rational too,

that contradicts assumptions.

The same is about z=xy and y=z/x. So, x+y

and xy are both irrational.

y - irrational

If z=x+y rational then y=z-x is rational too,

that contradicts assumptions.

The same is about z=xy and y=z/x. So, x+y

and xy are both irrational.

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