Thread: Solving 2 (1+ x^2)^2 = 10x. Sketching a graph of y = 2x / (1+x^2)^2.

1. Solving 2 (1+ x^2)^2 = 10x. Sketching a graph of y = 2x / (1+x^2)^2.

Hello, can any one help me solve for x by this equation:

2 (1+ x^2)^2 = 10x

I have no ideas ????

and how to draw f(x) = 2x / (1+x^2)^2

I'm using the calculator but did not get a clear pics for [0,2]

2. Originally Posted by huybinhs
Hello, can any one help me solve for x by this equation:

2 (1+ x^2)^2 = 10x

I have no ideas ????

and how to draw f(x) = 2x / (1+x^2)^2

I'm using the calculator but did not get a clear pics for [0,2]
1) There are no simple solutions to 2 (1+ x^2)^2 = 10x. Are you expected to solve it exactly or get decimal approximations of the solutions? Where has the equation come from?

2) What features of the graph are you expected to find and which of these are you stuck on?

3. 1) I found the equation base of I have calculated the f(ave) from 0 to 2 = 2/5

I have to set 2/5 equal to f(x) to find f(c)

2) I'm looking the area on the graph within 0, 2 and whatever the values of f(c) is.

4. Originally Posted by huybinhs
1) I found the equation base of I have calculated the f(ave) from 0 to 2 = 2/5

I have to set 2/5 equal to f(x) to find f(c)

2) I'm looking the area on the graph within 0, 2 and whatever the values of f(c) is.
f(x) = 2/5 has no simple solution, are you expected to get an exact solution?

What features of the graph of y = f(x) are you expected to find and which of these are you stuck on?

5. 1. I need to find f(c) = whatever the values are

2. I dont know how to graph to show the area within [0,2] and include the f(c) values!!!

6. $2 (1+ x^2)^2 = 10x$ has a very long exact solution. You could use an approximation method to find the approxiamate value of x to however many decimal places you want, like the Newton-Raphson Method.

Is it me or is what you are asking really confusing?
I'll do my best:

$\displaystyle \int_0^2 \frac{2x}{(1+x^2)^2}dx \ne \frac{2}{5}$

The integral from 0 to 2 doesn't equal 2/5. Can you show us what you did to get 2/5?

In the equation $f(x) = 2x / (1+x^2)^2$ where you substitute in values for f(x) and solve for x to get f(c), there will be no simple solution.

You can use approximation methods to find the values of f(c) to put into your graph, however I see no real solutions in what you are trying to calculate.