If a^3 + b^3 = 10 and a + b = 2, then find ab.
10=(a3+b3)
=(a+b)(a2-ab+b2) Factor differnce of cubes
=(a+b)(a2+2ab+b2-3ab)
=(a+b)((a+b)2-3ab)
=(2)(22-3ab)
so
5=4-3ab
1=-3ab
ab=-1/3
