2018 · Q12
If the sum of the squares of three consecutive natural numbers is 110, then the sum of their cubes is
Elementary MathematicsNumber System
- A625
- B654
- C684
- D725
Explanation
Let the numbers be n-1, n, n+1. Then (n-1)^2 + n^2 + (n+1)^2 = 3n^2 + 2 = 110, so n^2 = 36 and n = 6. The numbers are 5, 6, 7, and the sum of their cubes is 125 + 216 + 343 = 684. Hence option C.