Änderungen von Dokument BPE 3.4 Polynomgleichungen

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...	...	@@ -54,46 +54,32 @@
54	54
55	55	{{aufgabe id="Rückwärts lösen" afb="III" kompetenzen="K2,K5" quelle="Martina Wagner" lizenz="BY-SA"}}
56	56	(% class="abc" %)
57		-1. (((
58		-{{formula}}
59		-\begin{align*}
60		-\square x^3+\square=0\\
61		-\square x^3=\square \left| :2\\
62		-x^3=\square
63		-x=-2
64		-\end{align*}
65		-{{/formula}}
	57	+1. ((({{formula}}\square x^3+\square=0{{/formula}}
	58	+{{formula}}\square x^3=\square{{/formula}} | //:2//
	59	+{{formula}}x^3=\square{{/formula}}
	60	+{{formula}}x=-2{{/formula}}
66	66	)))
67		-1. (((
68		-{{formula}}
69		-\begin{align*}
70		-2x^3+\square x^2 &= 0 \\
71		-\square (x-\square) &= 0 \left|\left| \text{ SVNP }
72		-\end{align*}
73		-{{/formula}}
74		-
	62	+1. ((({{formula}}2x^3+\square x^2=0{{/formula}}
	63	+{{formula}}\square (x-\square)=0{{/formula}} || SVNP
75	75	{{formula}}x_{1,2}=\square; x_3=6{{/formula}}
76	76	)))
77		-1. (((
78		-{{formula}}\begin{align*}
79		-x^4+\square x^2+\square &= 0 & \left|\left|\text{ Subst.: } & x^2:=\square\\
80		-z^2+\square z + \square &= 0 & \left|\left|\text{ SVNP } &
	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	+)))
	74	+1. ((({{formula}}\begin{align*}
	75	+x^4+\square x^2+\square &= 0 & \left|\left|\text{ Subst.: }x^2:=\square\\
	76	+z^2+\square z + \square &= 0 & \left|\left|\text{ SVNP } \\
	77	+z_{1,2}=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
	78	+z_1=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}\\
	79	+\text{Resubst.: } \square := x^2\\
	80	+x_{1,2}^2=36 \Rightarrow x_{1,2}=\square\\
	81	+x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2
81	81	\end{align*}
82		-{{/formula}}
83		-
84		-{{formula}}
85		-\begin{align*}
86		-z_{1,2}&=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
87		-z_1&=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}
88		-\end{align*}
89		-{{/formula}}
90		-
91		-{{formula}}
92		-\begin{align*}
93		-&\text{Resubst.: } \square := x^2\\
94		-&x_{1,2}^2=36 \Rightarrow x_{1,2}=\square\\
95		-&x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2
96		-\end{align*}
97	97	{{/formula}})))
98	98	{{/aufgabe}}
99	99