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Find all solutions to the system

a + b = 14

a^3 + b^3 = 812 + ab

 Nov 4, 2022
 #1
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Hi Guest!
Hint: 

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

Thus, \(a^3+b^3=14((14)^2-3ab)=14(196-3ab)\)

So: 
\(\text{Given: }a^3+b^3 =812+ab \\ \implies 14(196-3ab)=812+ab\)

Now try to solve it from here :)

I hope this helps 

 Nov 4, 2022

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