2017 · Q18
If a³=335+b³ and a=5+b, then what is the value of a+b (given that a > 0 and b > 0) ?
Elementary MathematicsAlgebra
- A7
- B9
- C16
- D49
Explanation
From a = 5 + b: (5+b)³ − b³ = 335, i.e. 125 + 75b + 15b² = 335, so b² + 5b − 14 = 0. Factoring gives (b+7)(b−2) = 0; with b > 0, b = 2 and a = 7. Hence a + b = 9: option B.