perplexus.info :: Just Math : Given the Root, Find the Value

Given the Root, Find the Value (Posted on 2024-03-27)

Let x+1/x = √(47)

Find the value of:
x²⁰²³ - 2023*x²⁰¹⁹ + x²⁰¹⁵

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Finally got it

Comment 2 of 2 |

I tried a few ways unsuccessfully until I found the solution:

x^2023 - 2023x^2019 + x^2015

= x^2019 * (x^4 - 2023 + 1/x^4)

x + 1/x = √47

x^2 + 1/x^2 = √47^2 - 2 = 45

x^4 + 1/x^4 = 45^2 - 2 = 2023

x^2019 * (x^4 - 2023 + 1/x^4)

= x^2019 * (2023 - 2023)

= 0

Posted by Larry on 2024-03-27 10:44:16

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