The product of two consecutive negative integers is 210.
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The product of two consecutive negative integers is 210. What will be the sum of their cubes?
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Answer: D. D) -6119
The consecutive negative integers are -14 and -15 because (-14)*(-15) = 210. The sum of their cubes is (-14)^3 + (-15)^3 = -2744 + (-3375) = -6119.
Step-by-step Derivation:
Step 1: Let the integers be x and x+1. x(x+1) = 210 => x^2 + x - 210 = 0.
Step 2: Factoring gives (x + 15)(x - 14) = 0. Since the integers are negative, x = -15, and x+1 = -14.
Step 3: Compute sum of cubes: (-14)^3 + (-15)^3 = -2744 - 3375 = -6119.