The number of distinct integer solutions (x,y) of the equation |x+y|+|x−y|=2 , is
Question:
The number of distinct integer solutions (x,y) of the equation |x+y|+|x−y|=2 , is
The number of distinct integer solutions (x,y) of the equation |x+y|+|x−y|=2 , is
Options
Answer: 8
Explanation:
Step 1: Use the property: |x + y| + |x − y| = 2 × max(|x|, |y|) So the equation becomes: 2 × max(|x|, |y|) = 2 → max(|x|, |y|) = 1 Step 2: List all integer pairs with max(|x|, |y|) = 1 x = ±1, y = −1, 0, 1 → 6 pairs x = 0, y = ±1 → 2 pairs Total integer solutions = 6 + 2 = 8
Explanation:
Step 1: Use the property: |x + y| + |x − y| = 2 × max(|x|, |y|) So the equation becomes: 2 × max(|x|, |y|) = 2 → max(|x|, |y|) = 1 Step 2: List all integer pairs with max(|x|, |y|) = 1 x = ±1, y = −1, 0, 1 → 6 pairs x = 0, y = ±1 → 2 pairs Total integer solutions = 6 + 2 = 8
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