SOLUTION: If a is a irrational number and b is an rational number, prove that either (b − a) or (b + a) is
irrational.
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-> SOLUTION: If a is a irrational number and b is an rational number, prove that either (b − a) or (b + a) is
irrational.
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You can put this solution on YOUR website! Both must be irrational. Suppose that b-a is, on the contrary, a rational number r. Then a = b-r, contradiction because the sum/difference of two rational numbers is always rational (another way we can say this is that addition and subtraction are closed under rational numbers). The same logic applies to b+a = r.
