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Find one ordered pair $(x,y)$ of real numbers such that $x + y = 10$ and $x^3 + y^3 = 162 + x^2 + y^2.$

 Jul 10, 2024
 #1
avatar+867 
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(x,y) = (3 + 2*sqrt(2), 7 - 2*sqrt(2))

 Jul 10, 2024
 #2
avatar+174 
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The answers are \((5-i\sqrt{\frac{19}{14}},5+i\sqrt{\frac{19}{14}})\)

There are no real solutions. 

 Jul 11, 2024

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