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Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy|< /><9?>
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Find the number of distinct pairs of non negative integers (x,y) satis...
**Solution:**
To solve this problem, we need to consider two cases:
**Case 1:** 3 - 2xy ≥ 0
In this case, we have:
3 - 2xy = 2xy + 1 - 2xy = 1
Therefore, we need to find the number of distinct pairs of non-negative integers (x,y) that satisfy:
2xy ≤ 2 or xy ≤ 1
The pairs that satisfy this inequality are:
(0,0), (0,1), (1,0), (1,1)
**Case 2:** 3 - 2xy < />
In this case, we have:
3 - 2xy = -(2xy - 1)
Therefore, we need to find the number of distinct pairs of non-negative integers (x,y) that satisfy:
2xy - 1 ≤ -3 or 2xy ≤ -2 or xy ≤ -1
Since x and y are non-negative integers, the inequality xy ≤ -1 cannot be satisfied. Therefore, there are no solutions in this case.
**Final Answer:**
The number of distinct pairs of non-negative integers (x,y) satisfying |3 - 2xy| is 4.
To solve this problem, we need to consider two cases:
**Case 1:** 3 - 2xy ≥ 0
In this case, we have:
3 - 2xy = 2xy + 1 - 2xy = 1
Therefore, we need to find the number of distinct pairs of non-negative integers (x,y) that satisfy:
2xy ≤ 2 or xy ≤ 1
The pairs that satisfy this inequality are:
(0,0), (0,1), (1,0), (1,1)
**Case 2:** 3 - 2xy < />
In this case, we have:
3 - 2xy = -(2xy - 1)
Therefore, we need to find the number of distinct pairs of non-negative integers (x,y) that satisfy:
2xy - 1 ≤ -3 or 2xy ≤ -2 or xy ≤ -1
Since x and y are non-negative integers, the inequality xy ≤ -1 cannot be satisfied. Therefore, there are no solutions in this case.
**Final Answer:**
The number of distinct pairs of non-negative integers (x,y) satisfying |3 - 2xy| is 4.
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Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy|
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Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy| for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy| covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy|.
Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy| for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy| covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the number of distinct pairs of non negative integers (x,y) satisfying |3-2xy|.
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