perplexus.info :: Just Math : Roots in modified fractions

Roots in modified fractions (Posted on 2024-05-19)

If x₁,x₂,x₃ are the roots of equation x³-x-1=0 then compute

(2024+x₁)/(2024-x₁)+(2024+x₂)/(2024-x₂)+(2024+x₃)/(2024-x₃)

No Solution Yet Submitted by Danish Ahmed Khan

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

Thoughts

Comment 3 of 3 |

Using Wolfram Alpha to solve for the roots and plugging into the equation shows a result very close to 3.

I get 3.0000009573637536 which is very close to what Brian Smith found as the exact answer.

Replacing 2024 with other constants show similar results with results approaching 3 as the constant replacing 2024 gets larger. Not surprising since the limit is clearly 1+1+1=3

Posted by Larry on 2024-05-19 14:43:26

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info