if a+b=3 and a^2+b^2=6, what is a^3 + b^3

Answer 1

ab=((a+b)²-(a²+b²))/2

S=a^3+b^3
=(a+b)(a²-ab+b²)
=(a+b)(a²+b² - ((a+b)²-(a²+b²))/2))

All terms in the innermost parentheses are known, hence S.