Hei! :)
[tex]\left \{ {{x+y+z=3} \atop {x^{3} +x^{3} +z^{3} =3}} \right. \\=> x+y+z=3\\=> (x+y+z)^{3} ={x^{3} +x^{3} +z^{3}+3(x+y)(x+z)(z+y)[/tex][tex]=>(x+y)(y+z)(z+x)=8\\(3-x)(3-y)(3-z)=8 \\Dar\ (3-x)+(3-y)+(3-z)-3(x+y+z)=6\\=> |3-x|=|3-y|=|3-z|=2\\[/tex]
=> x, y, z ∈ {1, 5}
Dar x+y+z= 3
=> x, y, z ∈ {1}
