What values satisfy this equation: ((2x-7)/(x3+3))<(9/x)<=x²-5x+9?

In summary, the conversation is about finding the values of x that satisfy the equation ((2x-7)/(x3+3))<(9/x)<=x²-5x+9, where "<=" is the same as "and =". The speaker is having trouble finding the right values between (9/x)<=x²-5x+9, but otherwise has a solution. They hope for help in the future. Another person apologizes for not following the proper layout for posting in the homework help section. A solution is suggested, using the rational root theorem to factorize a quartic equation.
  • #1
andreynr6
1
0
Excuse me for my english;

Decide for all the x so this works out; ((2x-7)/(x3+3))<(9/x)<=x²-5x+9

where "<=" is the same as "and =".

Having some troubles getting the right values between (9/x)<=x²-5x+9, but otherwise it's fine..

hope you can help me!
 
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  • #2
For future reference, please use the layout given to you when starting a thread in the homework help section, particularly the "attempt at a solution" part.

To find where [tex]x^2-5x+9\geq 9/x[/tex] if you multiply through by x2 (a positive number for all real non-zero x) you will end up with a quartic that can be factorized easily using the rational root theorem. It should be easy from there where it's greater than zero.
 
  • #3
Sorry about that Mentallic. I moved his thread to Homework Help from a general math forum, and asked him to post more of his work. I should have posted a note here as well.
 
  • #4
Oh, no problem :smile:
 

1. What is the definition of absolute value?

The absolute value of a number is its distance from zero on the number line. It is always a positive value, regardless of the sign of the original number.

2. How do you calculate the absolute value of a number?

To calculate the absolute value of a number, you simply ignore the sign and take the positive value. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5.

3. What is the difference between absolute value and magnitude?

Absolute value and magnitude are often used interchangeably, but they have slightly different definitions. Absolute value refers to the numerical value of a number without its sign, while magnitude refers to the size or extent of a quantity or measurement.

4. How is absolute value used in real life?

Absolute value is used in various real life situations, such as determining the distance between two points, calculating temperature differences, and finding the error in measurements. It is also commonly used in solving equations and inequalities in mathematics.

5. Can the absolute value of a number ever be negative?

No, the absolute value of a number is always positive. However, when using absolute value in equations or inequalities, the resulting solution may be negative depending on the original problem and the operations performed.

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