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If A and B are positive integers, which of the following expressions is not an integer for certain?
- a)(2A2 – 2B2)/(A+B).
- b)(6B + 8A)/(3B + 4A).
- c)(3A – B)/(B - 3A).
- d)(A + B)/(A2 + B2 + 2AB).
- e)(A2 – B2)/(A - B).
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If A and B are positive integers, which of the following expressions i...
The best answer is D.
All the answers besides D are numbers after some simplification.Answer D = (A + B)/(A+B)2 = 1/(A+B), and this is a fraction of a number.
All the answers besides D are numbers after some simplification.Answer D = (A + B)/(A+B)2 = 1/(A+B), and this is a fraction of a number.
Most Upvoted Answer
If A and B are positive integers, which of the following expressions i...
The answer is (C).
To see why, let's simplify each expression:
a) (2A^2 - 3B^2) = an integer, since A and B are both integers.
b) (A + B)(A - B) = A^2 - B^2 = an integer, since A and B are both integers.
c) √(A^2 + B^2) = not necessarily an integer. For example, if A = 3 and B = 4, then √(A^2 + B^2) = √(9 + 16) = √25 = 5, which is an integer. However, if A = 4 and B = 7, then √(A^2 + B^2) = √(16 + 49) = √65, which is not an integer.
d) (A + B)^2 - 4AB = A^2 + B^2 - 2AB = (A - B)^2 = an integer, since A and B are both integers.
Therefore, the expression that is not necessarily an integer for certain is (C) √(A^2 + B^2).
To see why, let's simplify each expression:
a) (2A^2 - 3B^2) = an integer, since A and B are both integers.
b) (A + B)(A - B) = A^2 - B^2 = an integer, since A and B are both integers.
c) √(A^2 + B^2) = not necessarily an integer. For example, if A = 3 and B = 4, then √(A^2 + B^2) = √(9 + 16) = √25 = 5, which is an integer. However, if A = 4 and B = 7, then √(A^2 + B^2) = √(16 + 49) = √65, which is not an integer.
d) (A + B)^2 - 4AB = A^2 + B^2 - 2AB = (A - B)^2 = an integer, since A and B are both integers.
Therefore, the expression that is not necessarily an integer for certain is (C) √(A^2 + B^2).
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If A and B are positive integers, which of the following expressions is not an integer for certain?a)(2A2 – 2B2)/(A+B).b)(6B + 8A)/(3B + 4A).c)(3A – B)/(B - 3A).d)(A + B)/(A2 + B2 + 2AB).e)(A2 – B2)/(A - B).Correct answer is option 'D'. Can you explain this answer?
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