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Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 + b^2 = 6 + 2ab,$ then what is $a^3 + b^3?$

 Feb 20, 2024
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\((a+b)^2=a^2+b^2+2ab\\ 16=6+4ab\\ ab=\cfrac{5}{2}\)
Then 
\((a+b)^3=a^3+b^3+3ab(a+b)\\ 64=a^3+b^3+3(\frac{5}{2}){4}\\ \boxed{a^3+b^3=34}\)

 Feb 20, 2024

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