Question: Use a proof by contradiction to show that there is no rational number r for which r3 + r + 1 = 0. Assume that

Use a proof by contradiction to show that there is no rational number r for which r3 + r + 1 = 0. Assume that r = a/b is a root, where a and b are integers and a/b is in lowest terms. Obtain an equation involving integers by multiplying by b3. Then look at whether a and b are each odd or even.

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