2016 · Q15
If a³ = 117 + b³ and a = 3 + b, then the value of a + b is (given a > 0 and b > 0)
Elementary MathematicsAlgebra
- A7
- B9
- C11
- D13
Explanation
We have a³−b³ = 117 and a−b = 3 with a, b > 0. Using (a−b)³ = a³−b³−3ab(a−b) gives 27 = 117−9ab, so ab = 10. Then (a+b)² = (a−b)²+4ab = 9+40 = 49. Taking the positive root gives a+b = 7, option A.