Dux
Numbers up to 20
$$
\begin{flalign*}
& \textbf{Aufgabe 1 } & \\
a) \hspace{1cm} & \§§V1(3,15,3)§§ X + §§V2(3,12,3)§§ = §§V3(-30,30,3)§§ \\
b) \hspace{1cm} & \§§V4(3,15,1)§§ X + §§V5(3,12,2)§§ = §§V6(-30,30,4)§§ \\
c) \hspace{1cm} & \§§V7(3,15,3)§§ X + §§V8(3,12,3)§§ + §§V9(-30,30,3)§§ = 10 - §§V8(3,12,3)§§ X \\
d) \hspace{1cm} & \§§V3(5,25,5)§§ X + §§V11(3,12,5)§§ = §§V12(-30,30,1)§§ \\
e) \hspace{1cm} & \§§V10(2,12,2)§§ X + §§V11(2,12,2)§§ §§V12(-30,30,2)§§ = §§V10(2,22,2)§§ X + §§V11(3,12,3)§§ §§V12(-30,30,3)§§ \\
f) \hspace{1cm} & \§§V19(1,15,4)§§ X + §§V11(3,12,6)§§ = §§V12(-30,30,2)§§ + §§V12(10,30,2)§§ X \\
h) \hspace{1cm} & \§§V10(2,12,1)§§ X + §§V11(2,12,3)§§ + 2X - §§V12(0,30,2)§§ = §§V10(2,22,2)§§ X + §§V11(3,12,3)§§ §§V12(-30,0,3)§§ X + 6 \\
& \textbf{Aufgabe 2} & \\
a) \hspace{1cm} & \§§V3(2,12,2)§§ X^{2}-\frac{1}{ §§V5(1,10,1)§§ } X^{3} = 0 \\
b) \hspace{1cm} & \§§V1(3,12,2)§§ X^{2}-\frac{1}{ §§V1(1,10,1)§§ } X^{2} = 0\\
c) \hspace{1cm} & \ binom{21}{x}\sum_{x}^{x+12} ( X+2X - §§V2(5,20,1)§§ ) \\
d) \hspace{1cm} & \ X^{3} - §§V2(3,33,3)§§ X - §§V2(5,20,1)§§ + §§V3(2,12,2)§§ X^{2}-\frac{1}{ §§V5(1,10,1)§§ } x^{2} = 0 \\
e) \hspace{1cm} & \ e) \binom{21}{x}\sum_{x}^{x+12} ( X+2X - §§V2(5,20,1)§§ ) \\
& \textbf{Aufgabe 3} & \\
\left( §§V2(1,10,2)§§ a-b\right)^2 + \left(b- §§V0(2,20,2)§§ \right)^2 + \left( - §§V1(2,20,2)§§ c - §§V2(1,10,2)§§ \right)^2 = 0 \\
\left( §§V5(1,10,2)§§ a-b\right)^2 + \left(b- §§V6(2,20,2)§§ \right)^2 + \left( - §§V7(2,20,2)§§ c - §§V8(1,10,2)§§ \right)^2 = 0 \\
\left( §§V9(1,10,2)§§ a-b\right)^2 + \left(b- §§V4(2,20,2)§§ \right)^2 + \left( - §§V8(2,20,2)§§ c - §§V8(1,10,2)§§ \right)^2 = 0 \\
\left( §§V9(1,10,2)§§ a-b\right)^2 + \left(b- §§V4(2,20,2)§§ \right)^2 + \left( - §§V8(2,20,2)§§ c - §§V8(1,10,2)§§ \right)^2 = 0 \\
\end{flalign*}
$$