Änderungen von Dokument BPE 3.4 Polynomgleichungen

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...	...	@@ -59,33 +59,29 @@
59	59	{{formula}}x^3=\square{{/formula}}
60	60	{{formula}}x=-2{{/formula}}
61	61	)))
62		-1. ((({{formula}}
63		-\begin{align*}
64		-2x^3+\square x^2 &= 0 \\
65		-\square (x-\square) &= 0 \left|\left| \text{ SVNP }\\
66		-x_{1,2}=\square; x_3=6
67		-\end{*align}
68		-{{/formula}}
	62	+1. ((({{formula}}2x^3+\square x^2=0{{/formula}}
	63	+{{formula}}\square (x-\square)=0{{/formula}} || SVNP
	64	+{{formula}}x_{1,2}=\square; x_3=6{{/formula}}
69	69	)))
	66	+1. ((({{formula}}x^4+\square x^2+\square=0{{/formula}} || Subst.: {{formula}}x^2:=\square{{/formula}}
	67	+{{formula}}z^2+\square z + \square = 0{{/formula}} || SVNP
	68	+{{formula fontSize="larger"}}z_{1,2}=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}{{/formula}}
	69	+{{formula fontSize="larger"}}z_1=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}{{/formula}}
	70	+Resubst.: {{formula}}\square := x^2{{/formula}}
	71	+{{formula}}x_{1,2}^2=36 \Rightarrow x_{1,2}=\square{{/formula}}
	72	+{{formula}}x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2{{/formula}}
	73	+)))
70	70	1. ((({{formula}}\begin{align*}
71	71	x^4+\square x^2+\square &= 0 & \left|\left|\text{ Subst.: } & x^2:=\square\\
72	72	z^2+\square z + \square &= 0 & \left|\left|\text{ SVNP } &
73	73	\end{align*}
74		-{{/formula}}
75		-
76		-{{formula}}
77	77	\begin{align*}
78		-z_{1,2}&=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
79		-z_1&=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}
	79	+z_{1,2}=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
	80	+z_1=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}\\
	81	+\text{Resubst.: } \square := x^2\\
	82	+x_{1,2}^2=36 \Rightarrow x_{1,2}=\square\\
	83	+x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2
80	80	\end{align*}
81		-{{/formula}}
82		-
83		-{{formula}}
84		-\begin{align*}
85		-&\text{Resubst.: } \square := x^2\\
86		-&x_{1,2}^2=36 \Rightarrow x_{1,2}=\square\\
87		-&x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2
88		-\end{align*}
89	89	{{/formula}})))
90	90	{{/aufgabe}}
91	91