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help me systems of equations and inequalities



 
Post new topic   Reply to topic    math10.com - Online Math Forum Index -> Equations
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CATIAP



Joined: 25 Mar 2010
Posts: 1
PostPosted: Thu Mar 25, 2010 5:53 pm    Post subject: help me systems of equations and inequalities Reply with quote
16-4x^2>0
-3x^2<0
x^2-2x-3<0


(x+1)^2>3(x+2)+1
(x-1)^2+x(1-x)>2+(1-x)(x+1)
(1-x)^2<=1
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teacher
Site Admin


Joined: 09 Oct 2005
Posts: 151
PostPosted: Thu Mar 25, 2010 6:45 pm    Post subject: Reply with quote
Can you solve at least one?
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Shpresim



Joined: 26 Jul 2010
Posts: 2
PostPosted: Mon Jul 26, 2010 1:13 pm    Post subject: Re: help me systems of equations and inequalities Reply with quote
CATIAP wrote:
16-4x^2>0
-3x^2<0
x^2-2x-3<0


(x+1)^2>3(x+2)+1
(x-1)^2+x(1-x)>2+(1-x)(x+1)
(1-x)^2<=1



16-4x^2>0
-4x^2>-16 (divide by -4, the inequality sign changes)
x^2<4
-2<x<2

-3x^2<0 (divide by -3, the inequality sign changes)
x^2>0
we see that for any x the equation stays true
so the interval with solutions is (-∞,∞)

x^2-2x-3<0 (factor the left side of the inequality)
(x-3)(x+1)<0
-1<x<3
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