3) 0,5(3x2 -6)(x2 -25)(x+3) = 0
X1 = + wurzel 2 X2 = - wurzel 2
X3 = + 5 X4 = - 5
X5= -3
1) x^5 -3x^3 +x =0 x3=0
x^4-3x^2+1=0 y=x^2
y^2-3y + 1=0 p= - 3 q= 1
y₁= \( \frac{3}{2} \) + \( \sqrt{\frac{9}{4}-\frac{4}{4}} \) = \( \frac{3}{2} \) + \( \sqrt{\frac{5}{4}} \)
y2= \( \frac{3}{2} \) - \( \sqrt{\frac{9}{4}-\frac{4}{4}} \) = \( \frac{3}{2} \) - \( \sqrt{\frac{5}{4}} \)
Mit x=\( \sqrt{y} \)
folgt
X1= \( \sqrt{1,5 +\sqrt{\frac{5}{4}}} \)
X2= - \( \sqrt{1,5 +\sqrt{\frac{5}{4}}} \)
X3=0
X4= \( \sqrt{1,5 -\sqrt{\frac{5}{4}}} \)
X5= -\( \sqrt{1,5 +\sqrt{\frac{5}{4}}} \)