Fill in the details of the following proof that there exist irrational numbers a and b suc...

Fill in the details of the following proof that there exist irrational numbers a and b such that ab is rational.

Proof Let x = y = . If xy is rational, the proof is complete. (Explain.) Otherwise, suppose that, xy is irrational. (Why?) Let a = xy and b = . Consider ab. (How does this complete the proof?)

Is this proof constructive or nonconstructive?