\(已知：x^2-x+1=0,求：x^{2024}-x^{2023}的值。\)
\[
\begin{align*}
x^2-x+1=0 \\
x^2 = x-1 \\
\text{两边乘以x:} & x^3 = x^2-x \\
\text{由已知得:} & x^2-x = -1 \\
\text{即:} & x^3 = -1 \\
\\
\text{解：} & x^{2024}-x^{2023} \\
& =x^{2022} \cdot (x^2-x) \\
& =x^{2025} \\
& = (x^3)^{675} \\
& = (-1)^{675} \\
& = -1 \\
\end{align*}
\]