Finding the set of u such that

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In summary, the conversation discusses the logic behind finding a set of numbers that satisfy the inequality u(u-1) > 0. The correct approach is to consider two cases: u > 0 and u < 0. The solution is given as (-∞, 0) U (1, ∞), which means either u < 0 or u > 1. The conversation also touches upon the process of solving polynomial inequalities and references a helpful resource for further understanding.
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Hi. I'm having trouble understanding the logic behind finding a set of u for u(u-1) > 0. To solve these, I tend to factor as much as possible, then equate each expression to 0 (in this case to > 0) and solve, changing the > to < if I must divide by a negative number. I get u >0 and u > 1 but the solution is given as (-∞,0)U(1,∞), aka u>1 and u<0. Why does it say u<0?
Any help would be appreciated.

SOLVED. See below replies + http://tutorial.math.lamar.edu/Classes/Alg/SolvePolyInequalities.aspx
 
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1question said:
Hi. I'm having trouble understanding the logic behind finding a set of u for u(u-1) > 0. To solve these, I tend to factor as much as possible, then equate each expression to 0 (in this case to > 0) and solve, changing the > to < if I must divide by a negative number.
This is not the correct approach. If u(u - 1) > 0 then either
1) u > 0 AND u - 1 > 0. This leads to u > 0 AND u > 1, which simplifies to u > 1
OR
2) u < 0 AND u - 1 < 0. This leads to u < 0 AND u < 1, which simplifies to u < 0
1question said:
I get u >0 and u > 1 but the solution is given as (-∞,0)U(1,∞), aka u>1 and u<0.
No, (-∞, 0) U (1, ∞) does not mean u > 1 and u < 0, which no number can satisfy. There is no number that is simultaneously greater than 1 and negative.

(-∞, 0) U (1, ∞) means u < 0 or u > 1. The difference between "and" and "or" here is very significant.
1question said:
Why does it say u<0?
See above
 
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  • #4
1question said:
Hi Mark. OK, I generally understand the idea, except for why you would do 2) in the first place. The sign is > not <, so why did you do both? Thanks.
Because if a*b > 0, either both numbers have to be positive or both have to be negative. For example (-2)(-4) = + 8.
1question said:
EDIT: I believe I understand the process now.
http://tutorial.math.lamar.edu/Classes/Alg/SolvePolyInequalities.aspx is very helpful.
 
  • #5
Alright, so what you have here Is fun.
in fact when you open the parentheses you will get: u2 - u > 0.

Now to know when that happends you can simply solve what it should look like.
since the u^2 has a positive feature you can infer it will be a "smiling" parabule.
and you can clearly see the u(u-1) You can easly infere that the whole equation will equel zero at u=0 or u=-1

look at wolf ram alpha and see the discription fits.

After this you need to look at where the Y axis (the actual u(u-1)) is larger then 0.
You will find it does at numbers higher then 1 or lower then 0.

You're approax is deviding it into 2 separate the inequalities and I believe this way is easier and quicker.

Tell me if I am unclear.
 
  • #6
@ Spring. I figured it out already thanks to the link posted above. I appreciate the reply though!
 

1. What does it mean to "find the set of u such that"?

To "find the set of u such that" means to determine the values of the variable u that satisfy a given condition or equation. This is often done in mathematics or scientific research when studying relationships between variables.

2. How do you find the set of u such that?

The method for finding the set of u such that will depend on the specific problem or equation at hand. Generally, you will need to manipulate the equation or use mathematical tools such as substitution or elimination to solve for u.

3. What is the purpose of finding the set of u such that?

The purpose of finding the set of u such that is to better understand the relationship between variables and to solve for unknown values. This can be useful in making predictions, analyzing data, and developing theories in various fields of science and mathematics.

4. Can the set of u such that have multiple solutions?

Yes, the set of u such that can have multiple solutions. In fact, many equations or problems will have more than one solution for u. It is important to carefully consider the context of the problem to determine which solutions are relevant.

5. Are there any tips for finding the set of u such that more efficiently?

Some tips for finding the set of u such that more efficiently include carefully reviewing the given problem or equation, breaking it down into smaller parts, and using mathematical tools and strategies such as substitution and elimination. Additionally, practice and familiarity with mathematical concepts can also help improve efficiency in finding the set of u such that.

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