The product of two consecutive negative integers is 1122. what are the numbers?

(−33)(−34) = 1122

n × ( n + 1 ) = 1122 This gives n 2 + 1 n = 1122 subtracting both sides by 1122 gives n 2 + 1 n − 1122 = 1122 − 1122 or n 2 + 1 n − 1122 = 0 1122 = 33 × 34 ( n − 33 ) × ( n + 34 ) = 0 n = 33 or n = − 34 Negative factors are asked for, so reject n = 33 The factors are − 33 and − 34

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