\(p(x)=x^4 -13 \cdot x^2 +36\)
Lösungsweg ohne Substitution oder Vieta:
\(x^4 -13 \cdot x^2 +36=0\)
\(x^4 -13 \cdot x^2 =-36\)
\(x^4 -13 \cdot x^2 +(\frac{13}{2})^2=-36+(\frac{13}{2})^2\)
\([x^2 -(\frac{13}{2})]^2=\frac{25}{4} | ±\sqrt{~~}\)
\(1.)\)
\(x^2 -6,5=2,5 \)
\(x^2=9| ±\sqrt{~~} \)
\(x_1=3 \)
\(x_2=-3 \)
\(2.)\)
\(x^2 -6,5=-2,5 \)
\(x^2 =4 | ±\sqrt{~~} \)
\(x_3 =2 \)
\(x_4 =-2 \)