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Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^2 b + b^3 = -652. Find a+b.

 

Thank you!

 Mar 18, 2021
 #1
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algebraic solver => a = 7.44856, b = -3.44856, so a + b = 4.

 Mar 18, 2021
 #2
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a^3  +  3ab^2  =  679

 

3a^2b  + b^3   =  -652

 

Note  that   ( a + b)^3  =  ( a^3  + 3a^2b) + (3ab^2  + b^2) =  (a^3 + 3ab^2 )  + ( 3a^2b + b^3)

 

So

 

( a + b)^3  =   679  - 652

 

(a + b)^3  =  27         take the cube root of both sides

 

(a + b)  =  3

 

cool cool cool

 Mar 18, 2021

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