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

 Jun 27, 2024
 #1
avatar+129725 
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a + b = 4      square both sides

 

a^2 + 2ab + b^2  =16

 

a^2 + b^2 + 2ab = 16

 

6   + 2ab =  16

 

2ab =  10

 

ab = 5

 

 

a^3 + b^3  = (a + b) (a^2 + b^2  - ab) =  (4) (6 - 5)  =   4

 

 

 

cool cool cool

 Jun 27, 2024

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