Find the solution of three variables equality system x, y, z . a^3 + a^2 x + ay + z = 0 b^3 + b^2 x + by + z = 0 c^3 + c^2 x + cy + z = 0 Thank you so much


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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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