已知：\(m=\frac{\sqrt{2021}+1}{2}\)
求解：\((m^3-506m-503)^4\)
已知：\(m=\frac{\sqrt{2021}+1}{2}\)
可得：\(2m=\sqrt{2021}+1\)
\(2m-1=\sqrt{2021}\)
\(4m^2-4m+1=2021\)
\(4m^2-4m=2020\)
\(m^2-m=505\)
得:\(m^2=505+m\)
\(m^3 = m^2 \times m\)
\(m^3 = (505+m) \times m\)
\(m^3 = 505m+m^2\)
\(m^3 = 505m+505+m \)
得：\(m^3 =506m+506\)
原式：\((m^3-506m-503)^4\)
=\(506m+506-506m-503)^4\)
=\((2)^4\)
=\(16\)
即原式求解为：\(16\)。