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.
+118609
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.
