How Do You Solve the Equation e^x - x^3 + x^2 - 2x = 0?

[Cheman]

Does anyone know how to solve the following equation:

e^x-x^3+x^2-2x = 0.

Thanks in advance.

 

[arcnets]

x = 1.727780...
x = 4.098178...

 

[dextercioby]

It doesn't work that way...It's a transcendental equation.It's solutions are found only by approximation...Graphical method is the best to use...

Daniel.

 

[NeutronStar]

Does anyone know how to solve the following equation:

e^x-x^3+x^2-2x = 0.

Thanks in advance.

Do you know that without using LaTex you can still do superscripts using the [ sup ] [ /sup ] tags (without spaces)

For example. e^x can be written as e[ sup ]x[ /sup ] (to produce) e^x.

Type in [ sup ] (without the spaces), copy it, then just paste it as you type. Then add the slash to the trailing tags.

With just a little pasting your equation could look like this,...

e^x-x³+x²-2x = 0.

Or even encapsulate the whole mess in a larger font size llike so,...

e^x-x³+x²-2x = 0

The're even nestable. For example you could do something like the following without using latex at all.

e^(x2-y2)

You can also do subscripts the same way using [ sub ] [ /sub ]

Sorry. I just hate messy looking equations.

 

[dextercioby]

The good part is that,even written in this "horrible" way,it's still inteligible.Thankfully it didn't involve fractions... :tongue2:

Daniel.

 

[NeutronStar]

x = 1.727780...
x = 4.098178...

Yep, that's what I got too. These calculators never cease to amaze me.

 

[Integral]

One way to come up with a solution for this type of problem is to simply to isolate an x on one side of the equation. Then make a guess, following guesses are made by simply recomputing using the most recent result.

for example in this problem you can write

$$x = \frac { e^x -x^3+x^2} 2$$

With a starting guess of 1 the following sequence is generated
2.718281828
1.228890709
1.535886038
1.69065678
1.724461477
1.72755973
1.727765576
1.727778787
1.727779633
1.727779687
1.727779691


Trouble is this particular formulation will not generate the second point. It is required that the slope of the function be less then 1 in the region of the solution.

if you recast as

$$x= ln (x^3 -x^2 +2)$$

You get a fixed point at the second solution but is much slower in converging.

This process is know as a Fixed point solution. A web search may well provide more details.