Given the equation as follows
f(x) = x^3-4*x+1
First I will award frih10$ to the first person who can tell me the number of places where the equation crosses the x-axis
Second I will award frih30$ to the first person who can tell me the points to 10 decimal places where the equation crosses the X-axis
Finally, I will award frih$100 or 1/4 my total points, whichever is higher to the first person who can tell me all the equation that represent the exact points at which the equation crosses the X-axis
after 5 pages without the answer i will post a link to the answer
i cant understand your third requirement, but the solution of the first two requirements is below.
First I will award frih10$ to the first person who can tell me the number of places where the equation crosses the x-axis
It croses X-axis 3 times.
Second I will award frih30$ to the first person who can tell me the points to 10 decimal places where the equation crosses the X-axis
Point 1 (when y=0) : X= 0.254102 , or, x= 1.860806 , or, x= -2.114908
Please clear the third requirement, so that i may be able to answer it too.
well you did indeed get the first two which i expected to happen pretty quickly
so i will send the prize after this post.
as for clarification of the third section, i am asking for 3 mathematical formulas each one being the exact formula that represents the positions that you pointed out in part 2
where \() represents the square root, cubic root \3()
EG:
1.4142135624 => (the square root of 2) => \(2)
For the points where the equation crosses the X-axis
these numbers are abbreviations for the equation answers, the full answer keeps going, so an equation is necessary to represent the exact posititions
(0.254102)
(1.860806 )
(-2.114908 )
Is this what you are looking for on the third one:
0 = x^3-4*x+1
yes he needs that and there should be 3 answers like
x=0.254102
x=1.860806
x=-2.114908
but he needs the exact values
| MYP415 wrote: |
Is this what you are looking for on the third one:
0 = x^3-4*x+1 |
no. But i still cant understand what is the requirement.
I think you are asking to write those frectional answers in p/q form or in the form of some mathematical expression. If yes, please confirm.haha algrabra 2
That is sooo easy with a graphing calculator.
| imagefree wrote: |
| MYP415 wrote: | Is this what you are looking for on the third one:
0 = x^3-4*x+1 |
no. But i still cant understand what is the requirement.
I think you are asking to write those frectional answers in p/q form or in the form of some mathematical expression. If yes, please confirm. |
yes, i want the answers as some sort of mathematical expression that is the exact answer for the positions,
x=0.254102
x=1.860806
x=-2.114908
are abbreviations for infinite values
Example: .333 => 1/3
the exact value is 0.3333333....
point 3 repeating
i need the mathematical expression for the points on the axis.
when i see them i will post a web page with the answers on it here
The answers are extremely complex and that is why the prize is so high
Last edited by Dark-Tech on Sun Dec 16, 2007 6:55 pm; edited 1 time in total | Blaster wrote: |
haha algrabra 2
That is sooo easy with a graphing calculator. |
The first 2 were meant to be easy to draw people in
the third one is a lot harder than it sounds
If there are 5 more posts of people unable to figure out what im asking for i will post 1 of the three and the overall prize will be reduced by 1/3
so
the prize would become
66 instead of 100 or 1/6 of my total amountwow, this must really be a hard one if no one is even gonna try let alone get anywhere near the answer
I guess i was right that it was the hardest contest ever
I'll give it a try. It looks like you just want the three intercept values in fraction form, which may include pi, roots, or exponents. Is this correct?
| Dark-Tech wrote: |
wow, this must really be a hard one if no one is even gonna try let alone get anywhere near the answer
I guess i was right that it was the hardest contest ever |
The hardest thing is that we cant understand the requirement. Once we get the requirement, may be most of all can figure out the solution. | inventor wrote: |
| I'll give it a try. It looks like you just want the three intercept values in fraction form, which may include pi, roots, or exponents. Is this correct? |
That is exactly correct 
| imagefree wrote: |
| Dark-Tech wrote: | wow, this must really be a hard one if no one is even gonna try let alone get anywhere near the answer
I guess i was right that it was the hardest contest ever |
The hardest thing is that we cant understand the requirement. Once we get the requirement, may be most of all can figure out the solution. |
does that help any ?Here is the first solution
There are still 2 more, but the prize has been dropped to only 100, the 1/4 no longer is available | Quote: |
| the equation that represent the exact points at which the equation crosses the X-axis |
No need for i... click here. Approximate values for these equations are:
x1 = 0.2541016884
x2 = -2.114907541
x3 = 1.860805853
Obviously, for all these points y = 0yes those are the approximations but they are not the exact answers, i asked for the EXACT answers
and y does not = 0 it is close though
but close isn't good enough kinda like saying 300/900 = .3
which is wrong but close, .3333333 is close but still wrong, the best answer is 1/3
Should I make the link larger? Click here
Now tell me what's inexact about those equations. I only stated their approximate values to show that they match what came out of the graphing calculators... punch in the equations from the link to verify. | Arnie wrote: |
| Quote: | | the equation that represent the exact points at which the equation crosses the X-axis |
No need for i... click here. Approximate values for these equations are:
x1 = 0.2541016884
x2 = -2.114907541
x3 = 1.860805853
Obviously, for all these points y = 0 |
i didn't check them all but for
x3 = sqr(16/3)*cos(arcsin(sqr(27/256)/3)+(pi/6))
i kept coming up with 1.863246715That's because you've got your parentheses messed up. The expression you're giving in your post does not equal the equation for x3 I supplied. You're first dividing sqrt(27/256) by 3 and then taking the arcsin, while you're supposed to first take the arcsin of sqrt(27/256) and then divide by 3. Compare my equation for x3 to your expression: | Code: |
sqr(16/3)*cos(
arcsin(
sqr(27/256)/3
)
+(pi/6)
) |
Move the /3 to the outside of the ) that closes arcsin, and you have a correct expression for x3, yielding 1.860805853...
In my Console Calculator output below you can find all three valid expressions calculated to 50 digits. The used program is a freeware scientific calculator with 100-digit precision. Note that it uses asin instead of arcsin and sqrt instead of sqr.
I used the Options menu to set significant figures to 50. Here (click) is my output in a screenshot. Below it's in plain text, feel free to copy the commands and paste them into the calculator yourself. | Code: |
> sqrt(16/3)*sin(asin(sqrt(27/256))/3)
ans = 0.25410168836505241212977787984307247090591526081114
> sqrt(16/3)*cos((asin(sqrt(27/256))/3)+((5/6)*pi))
ans = -2.1149075414767557985156140607085439681237562633872
> sqrt(16/3)*cos((asin(sqrt(27/256))/3)+((1/6)*pi))
ans = 1.860805853111703386385836180865471497217841002576
> ans^3-(4*ans)+1
ans = -2.6004811855643251224256043391428812219097448696602e-101 |
Note the e-101 in the final answer where I calculated f(x3) using the 50-digit value for x3 1.8680... as shown above. e-101 means 101 zeroes (as in 0.00000000... etc) so that's a very small number. If the calculator were able to handle infinite decimals, it would be exactly 0. But it's not because we're using 50-figure approximate values of the exact equations I supplied earlier. It's hard to deny now that those equations are the exact solutions...
Bottom line, you're awfully careless for an 'exact' guy. And I @#$%^%$ wasted my time. So DarkTech, where've you been lately? There's a promise in your starting post you know...
well i can't find anything wrong so i will give you th prize, and i just haven't been around
All right, thanks 
