Prove that the system of equations below has only the solution ( x , y , z )

enrotlavaec 2022-06-24 Answered
Prove that the system of equations below has only the solution ( x , y , z ) = ( 1 , 1 , 1 ).
{ x + y 2 + z 3 = 3 y + z 2 + x 3 = 3 z + x 2 + y 3 = 3
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Answers (2)

Colin Moran
Answered 2022-06-25 Author has 21 answers
maybe you could find that x , y , z are symmetyical ,which means x , y , z have no difference with each other ,so x = y = z.you can solve this original equation by transform to x + x 2 + x 3 = 3,so x = 1,the so the only solution is ( x , y , z ) = ( 1 , 1 , 1 ).
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Celia Lucas
Answered 2022-06-26 Author has 5 answers
Finally, now I can solve my problem with my numbers, thanks!
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