Encontrar el intervalo solución de la siguiente inecuación cuadrática. \[ x^{2}-4 x-21>0 \]

Solve the equation. Check your solutions. (Enter your answers as a comma-separated list.) \[ 4 x^{2}(x-1)^{1 / 3}+10 x(x-1)^{4 / 3}=0 \] \( x=\square \)

Expand and simplify \( (r-9)(r-15) \)

\[ -\quad-x_{1}+2 x_{2}-7 x_{3}=4 \] 3. (30 points) Solve the system of linear equations using Gauss-Jordan method. Find the rank of the matrix of this system. Indicate dependent and independent variables. Find the fundamental solution set (write the answer as a linear combination of particular vectors) \[ \begin{array}{l}x_{1}+3 x_{2}+2 x_{3}-3 x_{4}=0 \\ 2 x_{1}+6 x_{2}+3 x_{3}-4 x_{4}=0 \\ 3 x_{1}+9 x_{2}+4 x_{3}-5 x_{4}=0\end{array} \]

\( ( 5 x + \ldots ) ( \ldots - 2 ) = ( ) ^ { 2 } - ( ) ^ { 2 } \)

Es sei \( \rho(x) \) eine Wahrscheinlichkeitsdichtefunktion (WD), die im Intervall \( [0 ; 2] \) gegeben ist durch \( \rho(x)=N_{0}(1 /(x+1)-1 / 3) \) und Null auBerhalb des Intervalls, \[ \rho(x)=\left\{\begin{array}{ll}N_{0}\left(\frac{1}{x+1}-\frac{1}{3}\right) & \text { fulr } x \in[0,2], \\ 0 & \text { sonst. }\end{array}\right. \] Bestimmen Sie die Konstante \( N_{0} \), so dass \( \rho(x) \) korrekt normiert ist.