**Hint:** Don't rush to do substitutions and alot of algebraic manipulations....stop and think. It is possible to find the value of A^{3} + B^{3} without first finding the values of either A or B.

**Solution Commentary:** Specific to the first problem:

1 x 2 = (A+B)(A^{2} + B^{2}) = A^{3} + B^{3} + AB(A+B)

But 1 = (A+B)(A+B) = A^{2} + B^{2} + 2AB = 2 + 2AB

This implies AB = - 1/2, which implies that A^{3} + B^{3} = 2 - (- 1/2) = 2 1/2

Feel free to go through all of the algebra to check this out...You should find that A = [1± SQRT(3)]/2, etc.

Now, you can try your hand at the second question.

Also, in the first question, is it helpful to note that A + B = 1 can be graphed as a line and A^{2} + B^{2} = 2 can be graphed as a circle....that intersect twice?