Online Course Discussion Forum

Math Challenge III 3.10 Algebra

 
 
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Math Challenge III 3.10 Algebra
by Raymond luo - Wednesday, 29 July 2020, 11:09 AM
 

I tried many things for this problem, like Simon's Favorite Factoring Trick which gave me $(x+1)(y+1)=6$ and $(x^3+1)(y^3+1)=18$ and substituting $u=x+y$ and $v=xy$ to get

$\begin{cases}  u(u^2-3v)+v^3=17 \\ u+v=5 \end{cases}$

Both didn't help that much however. Is there something that I'm missing?

 
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Re: Math Challenge III 3.10 Algebra
by Dr. Kevin Wang - Wednesday, 29 July 2020, 10:25 PM
 

SFFT does not help because this is not for integer solutions.

Your substitution does help. Write the first equation as $u^3- 3uv + v^3= 17$. This is as much hint as I need to give you. :)