Suppose x and y are irrational. Prove or disprove the following statement: “Either x + y or xy is irrational.”

Question

Suppose x and y are irrational. Prove or disprove the following statement: “Either x + y or xy is irrational.”
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Solution 1

This statement is not always true, and we can disprove it by providing a counterexample.

Consider the irrational numbers x = sqrt(2) and y = -sqrt(2). Both x and y are irrational numbers.

However, their sum x + y = sqrt(2) - sqrt(2) = 0, which is a rational number.

And their product xy = sqrt(2) Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

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