Änderungen von Dokument BPE 3.4 Polynomgleichungen

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...	...	@@ -59,34 +59,27 @@
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		-\end{align*}
67		-{{/formula}}
68		-
	62	+1. ((({{formula}}2x^3+\square x^2=0{{/formula}}
	63	+{{formula}}\square (x-\square)=0{{/formula}} || SVNP
69	69	{{formula}}x_{1,2}=\square; x_3=6{{/formula}}
70	70	)))
	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	+)))
71	71	1. ((({{formula}}\begin{align*}
72		-x^4+\square x^2+\square &= 0 & \left|\left|\text{ Subst.: } & x^2:=\square\\
73		-z^2+\square z + \square &= 0 & \left|\left|\text{ SVNP } &
	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
74	74	\end{align*}
75		-{{/formula}}
76		-
77		-{{formula}}
78		-\begin{align*}
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		-\end{align*}
82		-{{/formula}}
83		-
84		-{{formula}}
85		-\begin{align*}
86		-&\text{Resubst.: } \square := x^2\\
87		-&x_{1,2}^2=36 \Rightarrow x_{1,2}=\square\\
88		-&x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2
89		-\end{align*}
90	90	{{/formula}})))
91	91	{{/aufgabe}}
92	92