Änderungen von Dokument BPE 3.4 Polynomgleichungen

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• Seiteneigenschaften (1 geändert, 0 hinzugefügt, 0 gelöscht)

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...	...	@@ -54,49 +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		-
59		-{{formula}}
60		-\begin{align*}
61		-\square x^3+\square &= 0\\
62		-\square x^3 &=\square\quad \left| :2\\
63		-x^3 &= \square \\
64		-x &= -2
65		-\end{align*}
66		-{{/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}}
67	67	)))
68		-1. (((
69		-
70		-{{formula}}
71		-\begin{align*}
72		-2x^3+\square x^2 &= 0 \\
73		-\square (x-\square) &= 0 \left|\left| \text{ SVNP }
74		-\end{align*}
75		-{{/formula}}
76		-
77		-{{formula}}\Rightarrow x_{1,2}=\square; x_3=6{{/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}}
78	78	)))
79		-1. (((
80		-
81		-{{formula}}\begin{align*}
82		-x^4+\square x^2+\square &= 0 & \left|\left|\text{ Subst.: } & x^2:=\square\\
83		-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
84	84	\end{align*}
85		-{{/formula}}
86		-
87		-{{formula}}
88		-\begin{align*}
89		-\Rightarrowz_{1,2}&=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
90		-z_1&=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}
91		-\end{align*}
92		-{{/formula}}
93		-
94		-{{formula}}
95		-\begin{align*}
96		-&\text{Resubst.: } \square := x^2\\
97		-&x_{1,2}^2=36 \Rightarrow x_{1,2}=\square\\
98		-&x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2
99		-\end{align*}
100	100	{{/formula}})))
101	101	{{/aufgabe}}
102	102