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we-are-in-C-3-S-x-y-z-2i-1-and-xyz-2-xy-yz-xz-2-1-i-P-z-z-3-1-2i-z-2-2-1-i-2-show-that-a-b-c-is-solution-of-S-if-and-only-a-b-c-are-roots-of-P-

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Question Number 122658 by mathocean1 last updated on 18/Nov/20
we are in C^3 . (S): { ((x+y+z=2i−1 and xyz=2)),((xy+yz+xz=−2(1+i) )) :} P(z)=z^3 +(1−2i)z^2 −2(1+i)−2. show that (a,b,c) is solution of (S) if and only a;b;c are roots of P.
weareinC3.(S):{x+y+z=2i−1andxyz=2xy+yz+xz=−2(1+i)P(z)=z3+(1−2i)z2−2(1+i)−2.showthat(a,b,c)issolutionof(S)ifandonlya;b;carerootsofP.

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