inequalities help needed

Dec 2014
3
0
somewhere
sqrt(3x^2+3x+2)-1<=sqrt(x^2-x+1)
alright so this is the question,
so first i set that 3x^2+3x+2=>0 and i get that x=>-1 x<=-2
for x^2-x+1 i notice it's always above zero

next i do to the power of 2 on both sides and after solving what i got, i get the next boundry
(-1-sqrt(13))/6<x<(-1+sqrt(13))/6 and here i think im dont but the right answer is
x<=-2 -1<=x<(-1+sqrt(13))/6
if any one could explain why it is what it is, would be much helpful
 
Sep 2013
632
186
USA
(3*x^2 + 3*x + 2) is always positive and its minimum is 5/4. Are you sure you wrote the question correctly?
 
Dec 2012
1,145
502
Athens, OH, USA
Hi,
In future, please proof read your question. It took me a while to figure out what inequality you have. Here's the solution together with a graph of the situation:



 
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