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Question Number 153093 by naka3546 last updated on 04/Sep/21

F i n d t h e s o l u t i o n o f t h r e e v a r i a b l e s e q u a l i t y s y s t e m x, y, z .

a^{3} + a^{2} x + a y + z = 0

b^{3} + b^{2} x + b y + z = 0

c^{3} + c^{2} x + c y + z = 0

T h a n k y o u s o m u c h

Commented by MJS_new last updated on 04/Sep/21

{it}^{'} s linear for x, y, z

x = - (a + b + c)

y = a b + a c + b c

z = - a b c

Answered by mr W last updated on 05/Sep/21

a, b, c a r e t h e r o o t s o f f o l l o w i n g

c u b i c e q n . w . r . t . t :

t^{3} + {x t}^{2} + y t + z = 0

\Rightarrow a + b + c = - x \Rightarrow x = - (a + b + c)

\Rightarrow a b + b c + c a = y \Rightarrow y = a b + b c + c a

\Rightarrow a b c = - z \Rightarrow z = - a b c

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