How can I show that there are only finitely many solutions for the following system? x

lilmoore11p8 2022-07-16 Answered
How can I show that there are only finitely many solutions for the following system?
x 2 + y z = x
y 2 + z x = y
z 2 + x y = z
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Answers (1)

persstemc1
Answered 2022-07-17 Author has 18 answers
First assume x = y = z. That will give you two solutions.
Otherwise, one of the three unknowns differs from both others. If we assume x y and x z, use lab bhatteacharjee's hint to obtain two linear equations in x , y , z. You will notice that y = z and x = 1 follows from these and then there is a unique solution of the original equations (plus two others, by symmetry)
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