What two consecutive numbers have a product of 22,952?
Answer (3)
n ( n + 1 ) = 22952 n 2 + n − 22952 = 0 Δ = 1 2 − 4 ⋅ 1 ⋅ ( − 22952 ) = 91809 Δ = 91809 = 303 n 1 = 2 ⋅ 1 − 1 − 303 = 2 − 304 = − 152 n 2 = 2 ⋅ 1 − 1 + 303 = 2 302 = 151 n 1 + 1 = − 152 + 1 = − 151 n 2 + 1 = 151 + 1 = 152
Those numbers are -152 and -151 or 151 and 152.
x ( x + 1 ) = 22952 x 2 + x − 22952 = 0 Δ = 1 2 − 4.1. ( − 22952 ) = 1 + 91808 = 91809 x = 2 − 1 + 91809 = 2 − 1 + 303 = 2 302 = 151
Numbers are: 151 and 152
The two consecutive numbers that have a product of 22,952 are either -152 and -151 or 151 and 152. We derived these numbers by setting up a quadratic equation based on the product of consecutive integers. Using the quadratic formula, we solved for the integers, which yielded the pairs mentioned.
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