Solve the inequality; (x+3)[(x−1)^2 −x(x+(3/4))]+6+((7x^2 +29x)/4)>0 {Z.A}


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Question Number 164269 by Zaynal last updated on 15/Jan/22
$Solve the inequality; (x+3)[(x−1)^2 −x(x+(3/4))]+6+((7x^2 +29x)/4)>0 {Z.A}$
$S o l v e t h e i n e q u a l i t y;$ $(x + 3) [{(x - 1)}^{2} - x (x + \frac{3}{4})] + 6 + \frac{7 x^{2} + 29 x}{4} > 0$ ${Z . A}$
	Answered by manxsolar last updated on 15/Jan/22

	$p r i m e r t e r m i n o r a i z x = - 3$ $s e g u n d l t e r m i n o 24 + 7 x^{2} + 29 x = (7 x + 8) (x + 3) / 4$ $f a c t o r i z a n d o$ $(x + 3) [x^{2} - 2 x + 1 - x^{2} - \frac{3 x}{4} + \frac{7 x}{4} + \frac{8}{4}] ⟩ 0$ $(x + 3) [- 2 x + 1 + x + 2] ⟩ 0$ $(x + 3) [- x + 3] ⟩ 0$ $p o r - 1$ $(x + 3) (x - 3) ⟨ 0$ $p u n t o z c r i t i c o s$ $x = - 3$ $x . . = 3$ $- - - - - - - (- 3) - - - - - - - (+ 3) - - - - - - -$ $+ - +$ $m e p i d e n f (x) ⟨ 0$ $e n t o n c e s x \in< - 3; 3 >$ $s e a n x 1, x 2, x 3, . . . . . . . . x n r a i c e s d e l p o l i n o m i o = (x - x 1) (x - x 2 ((x - x 3) . . . . .$ $x n . . . . . . . . . . x 3 . . . . . . . x 2 . . . . . . . . . x 1 . . . . . . . . .$ $f (x) + - +$ $c o n d i c i o n e s u s o$ $t e r m i n o x p o s i t i v o$ $x 1, x 2, x 3, o r d e n a d o z e j e c a r t e z i a n o$
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