Question
How many integer pairs (x, y) satisfy the inequality
x2 + 4y2 < 100?Solution
y will lie in the range [-4, 4] When y = 4 or – 4, x will lie in the range [-5, 5] = 11 values. Total pairs = 22 When y = 3 or – 3, x will lie in the range [-7, 7] = 15 values. Total pairs = 30 When y = 2 or – 2, x will lie in the range [-9, 9] = 19 values. Total pairs = 38 When y = 1 or – 1, x will lie in the range [-9, 9] = 19 values. Total pairs = 38 When y = 0, x will lie in the range [-9, 9] = Total 19 pairs. Total pairs = 22 + 30 + 38 + 38 + 19 = 147
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