|
|Store|
|
|
|
|
|
|
|
CTK Exchange
Kratoz
guest
|
May-15-02, 06:39 PM (EST) |
|
|
"Single Rational Solution Problem"
| |
I would like some help to find the solution to the following: sqrt(1+114(n)^2)=x ;x is rational; find n Thank you to anyone who can help. |
|
|
Alert | IP |
Printer-friendly page | Edit |
Reply |
Reply With Quote | Top |
|
|
alexb
Charter Member
726 posts |
May-15-02, 07:56 PM (EST) |
    |
1. "RE: Single Rational Solution"
In response to message #0
| |
>I would like some help to find the solution to the
>following:
>
>sqrt(1 114(n)^2)=x ;x is rational; find n
>
>Thank you to anyone who can help. Is n integer? If so, you may claim that any rational x is in fact integer. Assuming n is integer, think of its last digit. What may it be? Squares may end only with certian digits. You may also want to find out about casting out 9. |
|
|
Alert | IP |
Printer-friendly page | Edit |
Reply |
Reply With Quote | Top |
|
|
Harry Hickey
guest
|
May-17-02, 10:59 PM (EST) |
|
|
2. "RE: Single Rational Soln Problem"
In response to message #0
| |
>I would like some help to find the solution to the
>following:
>
>sqrt(1+114(n)^2)=x ;x is rational; find n
>
>Thank you to anyone who can help.
Rewrite the equation as:
1+114*n^2 = x^2
This is a "Pell" equation, and has an infinity of solutions with x and n both integers. Pell equations are often discussed in books on elementary Number Theory, as well as books on Continued Fractions (since the CF is the tool used to solve pell's equation). Or you might try "Pell's Equation" on the Web and see what you find.
Finally, a brute-force method is to write a small BASIC program that scans over successive values of n until it hits one that satisfies your original equation -- it won't run forever (look for a solution at about n = 19600). You must be careful about your integers & reals, though. As a solution to a math problem, it's stupid, but you may learn something about programming! |
|
|
Alert | IP |
Printer-friendly page | Edit |
Reply |
Reply With Quote | Top |
|
|
You may be curious to visit the old CTK Exchange archive.
|Front page|
|Contents|
|Store|
Copyright © 1996-2018 Alexander Bogomolny
[an error occurred while processing this directive]
|
Advertise
|
Printer-friendly copy
Email this topic to a friend