Question: Prove that for each real number x, (xmiddot+ squareroot 2) is irrational or (-x + squareroot 2) is irrational. Generalize the proposition in Part (a)

Prove that for each real number x, (xmiddot+ squareroot 2) is

Prove that for each real number x, (xmiddot+ squareroot 2) is irrational or (-x + squareroot 2) is irrational. Generalize the proposition in Part (a) for any irrational number (instead of just squareroot 2) and then prove the new proposition

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