Question:
If
\[ a+b=3 \] and \[ ab=2, \] then \[ a^3+b^3= \]
(a) 6
(b) 4
(c) 9
(d) 12
Solution:
Using identity:
\[ a^3+b^3 = (a+b)^3-3ab(a+b) \]
Substituting the given values:
\[ a^3+b^3 = 3^3-3(2)(3) \]
\[ =27-18 \]
\[ =9 \]
Hence, the correct answer is:
\[ \boxed{9} \]