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If 4ab = 4 is irrational, then a is irrational or b is irrational?

1) a is irrational
2) is irrational
3) both a and b are irrational
4) neither a nor b is irrational

User Leoz
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1 Answer

1 vote

Final answer:

Both a and b must either be rational or irrational to satisfy the equation 4ab = 4 being irrational; however, the statement does not provide enough data to ascertain which is the case.

Step-by-step explanation:

The statement 4ab = 4 is irrational suggests that the product of a and b when multiplied by 4 is an irrational number. If we divide both sides of the equation by 4, we get ab = 1. For this equation to hold, if one of the numbers, say a, is rational (meaning it can be expressed as the ratio of two integers), then b must also be rational because the ratio of two rationals is always rational. On the other hand, if a is irrational, then b must be irrational as well to maintain the product as an irrational number. Therefore, the conclusion is that either both a and b are rational or both a and b are irrational. Hence, the correct option is either both are rational or both are irrational, but the statement does not have enough information to determine which is the actual case.

User Yotommy
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