2014 · Q35
Consider the following statements:
- 1(a − b − c) is one of the factors of 3abc + b³ + c³ − a³.
- 2(b + c − 1) is one of the factors of 3bc + b³ + c³ − 1.
Which of the above statements is/are correct?
Elementary MathematicsAlgebra
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
a³ + b³ + c³ − 3abc = (a + b + c)(…); substituting −b, −c gives (a − b − c) as a factor of a³ − b³ − c³ − 3abc, i.e. of 3abc + b³ + c³ − a³. Similarly (b + c − 1) divides 3bc + b³ + c³ − 1.