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

 Jun 16, 2024
 #1
avatar+129743 
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a + b = 4

square both sides

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

 

a^2 + b^2 = 6

 

So

 

6 = 16 - 2ab

-10 = -2ab

5 = ab

-5 = -ab

 

a^3 + b^3  =  

(a + b) ( a^2 + b^2 - ab) =

(4) (6 -  - 5)

(4) (11)  = 

44

 

cool cool cool

 Jun 16, 2024

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