The sum of a number’s square, its cube, and its next number’s cube is 205. What is the number?
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Answer:
x = 4
Step-by-step explanation:
x² + x³ + (x + 1)³ = 205
x² + x³ + x³ + 3x² + 3x + 1 = 205
2x³ + 4x² + 3x + 1 = 205
2x³ + 4x² + 3x + 1 - 205 = 0
2x³ + 4x² + 3x - 204 = 0
(x - 4)(2x² + 12x + 51) = 0
x - 4 = 0
x = 4
4² + 4³ + 5³
16 + 64 + 125
205
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