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x^2-x+1=0
x^2-x+1÷4=-3÷4
(x-1÷2)^2=-3÷4
x-1÷2=√-3÷4| or=-√-3÷4|
İf positive ->x=√-3÷4|+1÷2)

İf negative x=-√-3÷4|+1÷2

x^2024-x^2023=x•x^2023-x^2023
=(x-1)•x^2023
(First equation is x^2-x+1=0 for this reason x^2=x-1)

When we place the x's we found into the equation, the answers are-->
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Aposefendi
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If we use the formula a³+b³ we get (a+b)(a²-ab+b²) if a²-ab + b² is zero it implies a³=-b³ by putting value x=-1

shaswat
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The answer is -1. If x²-x+1=0 then x³+1=0 but x≠-1. Then x³=-1 and if we plug it to the second equation we get From the first equation we get x²-x=-1 so the answer is -1

baranalitul
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x^2 = x-1. Factor out x^2024 - x^2023 you get x^2023 multiply x - 1. Substitute x-1 with x^2. Answer is x^2025

msam
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X² - X + 1 = 0
Multiply everything by x²⁰²²
Law of indices states a^x*a^y = a^(x+y)
Therefore
x²⁰²²(x²) - x²⁰²²(X) + x²⁰²²(1) = 0 =
x²⁰²⁴ - x²⁰²³ + x²⁰²² = 0
Subtract by x²⁰²²
x²⁰²⁴ - x²⁰²³ = -x²⁰²²
To solve for x,
x²⁰²⁵

x = ½ +- i(√3)/2
arg(x) = arctan(√3) = π/3
x²⁰²⁵ = (cos(2025 × π/3) + isin(2025 × π/3)
x²⁰²⁵ = cos(673π) + isin(673π) =
x²⁰²⁵ = cos(π + 672π( + isin(π + 672π)
x²⁰²⁵ = cosπ + isinπ = -1

loghtsy
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-x^2022

You can calculate x using the quadratic formula:

a = 1 b = -1 and c = 1

Delta = b^2 -4ac = 1 - 4
= -3

X = (-1 ± √3i)/2

mrmimi
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The answer should be -1 .
We have equation x²-x+1=0 and on transposing x²=x-1 .now from equation x^2024-x^2023 on taking x^2023 common , we got x^2023(x-1) which is equal to x^2025 . Same thing can be obtained on multiplying x^2023 to x²=x-1 we get x^2024-x^2023=c^2025 . And on multiplying x^2022 to x²=x-1 we get x^2024-x^2023 = -x^2022 hence x^2025=-x^2022 on solving we get answer as -1

maheshgupta
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The question has multiple answers


Both x²⁰²⁵ and -(x²⁰²²) are correct answers

Vg
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x^2-x+1=0, operating this quadratic equation by subtracting 1 from both sides, we would have x^2-x= -1, here comes the interesting part, if you realize x^2-x, they have the difference of an exponent and if they can see, too x^2024-x^2023 they are also carried with an exponent of difference but x^2-x= -1, let us also keep in mind that x^2-x they are carried with an exponent of difference buuuut too x^2024-x^2023 they are carried with an exponent by difference, I mean practically x^2-x and x^2024-x^2023 they are equal because in those 2 equations and in each one they take an exponent by difference and how x^2-x taking an exponent as a difference is equal to -1 then x^2024-x^2023= -1 because also like x^2-x they are carried with an exponent by difference, be careful, the problem does not ask you to find the values ​​of x, if not, it asks you what that subtraction of x with giant exponents is equal to

messimessi
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Although -1 is the value of x. If you substitute this value in the first equation you will get 3 instead of 0

AhsanRafi-nklo
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the answer is impossible😅x=1/2+-sqrt-3/4

williamhøyland-us
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Ans is -1...roots of that equation are -W and -W^2...solving 2nd equation we get x^2025...fill

tanveersharma