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December 22nd, 2010, 04:46 PM  #1 
Member Joined: Dec 2010 From: Viet Nam and US Posts: 36 Thanks: 0  Inequality solve
Hi guys I'm new, I need help in this topic Solve: [color=#008000] (1)[/color] I'm trying to use another variable to replace x (sorry about my English, I'm Asian, I just love math ). So I do: Let [color=#008000] (2)[/color] [color=#008000] (1)(2)[/color] And I'm stuck there 
December 22nd, 2010, 05:38 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2207 
Where did "10t" spring from? You have 3x = t²  2, so multiply the original equation by 3 and then substitute for 3x throughout and find the nonnegative values of t that satisfy the inequality, etc.

December 22nd, 2010, 05:56 PM  #3  
Member Joined: Dec 2010 From: Viet Nam and US Posts: 36 Thanks: 0  Quote:
About where "10t" comes from, I mistyped, it must be "10xt" let me explain: We have and The original inequality can be rewritten: or And that's how I came up, I need another better solution I guess  
December 22nd, 2010, 06:10 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2207 
That's precisely what I gave you  multiply the original equation by 3, etc. You'll find it easy if you try it. Alternatively, plot the graph of the lefthand side of the original equation.

December 22nd, 2010, 07:33 PM  #5  
Member Joined: Dec 2010 From: Viet Nam and US Posts: 36 Thanks: 0  Re: Quote:
Multiply both sides by 3, substitute and simplify: Factor out (I don't know how to explain, just see the line below) the result, we have: Listed the solutions orderly, we have: So in order to make the equation satisfy, we have to pick: But that is the way we pick t, how about x? The main reason is to solve x. I think I mislead somewhere!  
December 22nd, 2010, 07:48 PM  #6  
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2207  Quote:
 
December 22nd, 2010, 08:09 PM  #7  
Member Joined: Dec 2010 From: Viet Nam and US Posts: 36 Thanks: 0  Re: Quote:
Multiply both sides by 3, substitute and simplify: Factor out and we have: Listed the solutions orderly, we have: So in order to make the equation satisfy, we have to pick: I think it's ok now, but how about x? That solution now works for t only. I'm not sure what you mean by "only nonnegative values of t are of interest" (language limit I'm sorry).  
December 22nd, 2010, 08:52 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2207 
Your (x + 1)² should be (t + 1)², but can be omitted (just solve 2t² + 10t + 5 ? 0). You solved incorrectly. You need t ? 0, so 0 ? t ? (3 + ?35)/2. Hence 0 ? t² ? (22  3?35)/2, i.e., 0 ? 3x + 2 ? (22  3?35)/2, and so 2/3 ? x ? (6  ?35)/2. 
December 22nd, 2010, 09:00 PM  #9  
Member Joined: Dec 2010 From: Viet Nam and US Posts: 36 Thanks: 0  Re: Quote:
 

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