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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Solution

| Comment 1 of 2

factor x^2019 out of the expression to be evaluated:

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

Now take the equation and square both sides:

x^2 + 2 + 1/x^2 = 47

x^2 + 1/x^2 = 45

and square both sides again

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

x^4 + 1/x^4 = 2023

Substitute this into the expression

x^2019(2023-2023)

and the answer is 0.

Posted by Jer on 2024-03-27 09:15:43

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