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

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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

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