Weg, wenn keine Substitution verlangt ist:
\( x^4 - \frac{25}{36} x^2 + \frac{1}{9} =0\)
\( x^4 - \frac{25}{36} x^2 =- \frac{1}{9}\)
\( x^4 - \frac{25}{36} x^2+(\frac{25}{72})^2 =- \frac{1}{9}+(\frac{25}{72})^2 \)
\(( x^2 - \frac{25}{72})^2 =\frac{49}{5184} |±\sqrt{~~} \)
1.)
\( x^2 - \frac{25}{72} =\frac{7}{72} \)
\( x^2 =\frac{4}{9} |±\sqrt{~~} \)
\( x_1=\frac{2}{3} \)
\( x_2=-\frac{2}{3} \)
2.)
\( x^2 - \frac{25}{72} =-\frac{7}{72} \)
\( x^2 = \frac{1}{4} |±\sqrt{~~} \)
\( x_3=\frac{1}{2} \)
\( x_4=-\frac{1}{2} \)
