calling mathematicians

[icemonster]

x^4 = 1.02, solve for x. how is this done? and how do you check it?

 

[Mihail]

x = 1.02 ^ (1/4) . Very easy for me.

 

[icemonster]

not quite, you see when that answer is .255, but when you raise to ^4, it gives something else entirely.

 

[kevlray]

I did not like the answer the Windows calculator was giving me. So I used an Excel function and came up with 1.004963 which seems to work.

 

[David R]

Where are you getting 0.255? That would be x*4 = 1.02

x = 1.004962932

 

[stopher]

I agree with Mihail. 1.02^(1/4) = 1.0049629...

You can calculate it easily by pressing the square root button twice.

You can test it by squaring it twice.

 

[Mihail]

) This question is a serious one ? I don't think so.
Taylor's theorem say that you can solve this equation for any number of digits (with any precision)
The Taylor's formula is used by programmers in order to solve this type of equations.

So, you can calculate all your life SQRT4 from 1.02 but, when you will check the result (result * resul * result * result) still will don't much with 1.02.
Just, year after year, you will be a little bit more precise. The rest (Rn) will be, year after year, smaller.

So you have a bit of work in order to check if we (Taylor and me) are on the right track.
Good luck ! ))))))

 

[Mihail]

And is not necessary to be mathematician to know that X can't be smaller than 1.
First 8 years of school are enough.

 

[David R]

) This question is a serious one ? I don't think so.
Taylor's theorem say that you can solve this equation for any number of digits (with any precision)
The Taylor's formula is used by programmers in order to solve this type of equations.

So, you can calculate all your life SQRT4 from 1.02 but, when you will check the result (result * resul * result * result) still will don't much with 1.02.
Just, year after year, you will be a little bit more precise. The rest (Rn) will be, year after year, smaller.

So you have a bit of work in order to check if we (Taylor and me) are on the right track.
Good luck ! ))))))

No, seriously. We have the answer. stopher and I figured it in 3 seconds with a calculator/Excel. No theorem or graphs needed for such a simple problem.

I suspect the OP simply confused exponential notation for multiplicative notation, thus the 0.255.

 

[spikepl]

And the approximate solution of (1+ε)^(1/4), where ε<<1 is 1 + ε /4 which in this case is 1.005

 

[dhop1990]

http://www.wolframalpha.com/input/?i=x^(1/4)&lk=4

Everything you would ever want to know about the function. If you are going to user a Taylor, McLauren, or any other type of series you might as well go all the way and use an integral to sum the series over infinite approximations.

The graph gives you an idea of the how the function would react to a change in x values.

For a former math major that is interested in Series representations and imaginary number, wolframalpha.com is an excellent resource; but it's also great for simple answers. It came in handy with physics and and math courses when I would get stumped.

Practical solution as others have stated:

X^4 = y then
x^2= y^(1/2) then
x= (y^(1/2))^(1/2)= y^.25

 

[Dick7Access]

x = 1.02 ^ (1/4) . Very easy for me.

The job you are looking for, does it involve power press

 

[AnthonyGerrard]

I think there are 4 roots, so

1.0049629
-1.0049629
1.0049629i
-1.0049629i