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
$we are in C^3 . (S): { ((x+y+z=2i−1 and xyz=2)),((xy+yz+xz=−2(1+i) )) :} P(z)=z^3 +(1−2i)z^2 −2(1+i)−2. show that (a,b,c) is solution of (S) if and only a;b;c are roots of P.$
$w e a r e i n C^{3} .$ $(S) : {\begin{cases} x + y + z = 2 i - 1 a n d x y z = 2 \\ x y + y z + x z = - 2 (1 + i) \end{cases}$ $P (z) = z^{3} + (1 - 2 i) z^{2} - 2 (1 + i) - 2 .$ $s h o w t h a t (a, b, c) i s s o l u t i o n$ $o f (S) i f a n d o n l y a; b; c a r e$ $r o o t s o f P .$
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