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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?

 May 1, 2024
 #1
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a2+b2=6+2aba2+2ab+b2=6+4ab(a+b)2=6+4ab

But a + b = 4, so

42=6+4abab=52

 

Then consequently a3+b3=(a+b)33ab(a+b)=433524=34.

 May 1, 2024

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