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I need help with a system

 

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and a^3 - 3ab^2 = 673.  Find a - b.

 Jan 30, 2023
 #5
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a^3 + 3ab^2 = 679 and a^3 - 3ab^2 = 673

 

\(a^3 + 3ab^2 = 679\qquad and \qquad a^3 - 3ab^2 = 673 \)

 

add them and get


\(2a^3= 1352\\ a^3=676\)

 

factor(676) = 2^2*13^2  not much help

 

subtract them

 

\(6ab^2=6\\ ab^2=1\\ \sqrt[3]{676}\;\;b^2 = 1\\ b^2=676^{-1/3}\\ b=676^{-1/6}\\ b=26^{-1/3}\\ \)

 

\(a-b=\sqrt[3]{676}-\sqrt[3]{\frac{1}{26} }\)

 

I could easily have made a careless mistake but I strongly think you may have made a copy error when you wrote the question in.

 Jan 30, 2023

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