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Let a and b be real numbers such that a+3ab=679 and 3a2 b + b3 = -652  Find a + b.

 

Thanks
 

 Mar 14, 2021
edited by Guest  Mar 14, 2021
 #1
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Add the 2 equations up:

\(a^3+3ab^2+3a^2b+b^3=27\)\(\)

Notice that \((a+b)^3=a^3+3ab^2+3a^2b+b^3\)\(\) by the binomial theorem. Therefore, \((a+b)^3 = 27 \rightarrow \boxed{a+b=3}\)

 Mar 14, 2021
 #2
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Thank you

Guest Mar 14, 2021

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