# let n is non-negative number so the equations ( x 2 </msup> + 1

jistefaftexia99kq6 2022-05-14 Answered
let $n$ is non-negative number so the equations$\left({x}^{2}+1{\right)}^{2}+n=yz+1$$\left({y}^{2}+1{\right)}^{2}+n=zx+1$$\left({z}^{2}+1{\right)}^{2}+n=xy+1$have $\left(x,y,z\right)$ real solution.find all solutions for the non-negative n that make $\left(x,y,z\right)$ are real numbers and find $\left(x,y,z\right)$ also
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## Answers (1)

Bumanro5mv
Answered 2022-05-15 Author has 9 answers
Hint: First argue why x,y,z must have same sign. Now subtract any one equations from the other and conclude that x=y=z is only possible solution. Substitute in anyone equation and find the solution.
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