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Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.

 Apr 23, 2024
 #1
avatar+128772 
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a^3 + 3ab^2  =  679       (1)

 

3a^3 - ab^2  =  615     →   9a^3 - 3ab^2  = 1845      (2)

 

Add (1) , (2)   and we  have

 

10a^3  =  2524

 

a^3  =  2524 / 10

 

a =    (252.4)^(1/3)

 

Sub this into   (1)

 

(2524/10) + 3 (252.4)^(1/3) b^2  = 679      solving this  for b produces

 

b = -4.74353  or b = 4.74353

 

a - b  = ( 252.4)^(1/3) + 4.74353  ≈   11.06

 

a - b =  (252.4)^(1/3) - 4.74353 ≈ 1.576

 

cool cool cool

 Apr 23, 2024

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