Cube Consecutive
Algebra
Level
2
There are four consecutive integers such that the sum of the cubes of first three numbers is equal to the cube of the fourth number. Find the sum of the four numbers.
The answer is 18.
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1 solution
If we take a as the integer, we have the four consecutive numbers: a , a + 1 , a + 2 , a + 3 . So writing and simplifying the equation we have a 3 − 6 a − 9 = 0 , which has factors ( a 2 + 3 a + 3 ) ( a − 3 ) , the first one doesn't have any integer solution, the second one gives a = 3 So the four numbers are 3 , 4 , 5 , 6 and the sum is 1 8