Algebra

Question

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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 $a^3 + b^3?$

booboo44 Feb 20, 2024

EnormousBighead · Answer 1 · 2024-02-20T04:42:59

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