consider the function f(x)=3x^2-12/x^2+2x

Hello, and welcome to FMH!

In order to determine which values of \(x\) result in \(f(x)=3\), we should solve the following equation:

[MATH]f(x)=3[/MATH]
[MATH]3x^2-\frac{12}{x^2}+2x=3[/MATH]
I would multiply through by \(x^2\) and arrange in standard form:

[MATH]3x^4+2x^3-3x^2-12=0[/MATH]
At this point, I would consider numeric root finding techniques. Are you sure you copied the problem correctly?
 
First you should look to see if you can see the solution. You should then try the ration root theorem.

You must do this first. Unfortunately these two procedures will not give you any roots. At this point you must approximates the roots. Which methods have you learned to do that?
 
mcall said:
consider the function f(x)=3x^2-12/x^2+2x
if f(x)=3,what is x?
Click to expand...
I'm wondering if you meant f(x)=(3x^2-12)/(x^2+2x). If you did, the parentheses are essential.

In that case, you have to solve (3x^2-12)/(x^2+2x) = 3, which transforms to 3x^2 - 12 = 3(x^2 + 2x). This is easy to solve -- or, if you prefer, impossible. At any rate, it's more interesting pedagogically. Maybe that makes this interpretation more likely ...

Actually, I initially solved it a different way, simplifying the LHS first. It's interesting to try both approaches.
 
I wrote it wrong. It should have been f(x)=(3x^2-12)/(x^2+2x) so Mr.Peterson's explanation is what I needed but thanks anyways!
 
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