lehrkraefte:blc:miniaufgaben:kw07-2017

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lehrkraefte:blc:miniaufgaben:kw07-2017 [2017/02/05 12:51] – created Ivo Blöchligerlehrkraefte:blc:miniaufgaben:kw07-2017 [2020/08/09 13:16] (current) – external edit 127.0.0.1
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 +==== 13. Februar 2017 bis 18. Februar 2017 ====
 +=== Dienstag 14. Februar 2017 ===
 +Vereinfachen Sie:
 +  - $$\left(x^{\frac{8}{3}}\right)^{\frac{13}{16}}: x^{\frac{3}{2}}$$
 +  - $$\left(x^{-\frac{3}{5}}\right)^{-\frac{115}{18}}: x^{\frac{3}{2}}$$
 +  - $$\left(x^{\frac{6}{5}}\right)^{\frac{1}{9}}\cdot x^{\frac{5}{3}}$$
 +
 +<hidden Lösungen>
 +  - $$x^{\frac{2}{3}}$$
 +  - $$x^{\frac{7}{3}}$$
 +  - $$x^{\frac{9}{5}}$$
 +</hidden>
 +
 +
 +=== Donnerstag 16. Februar 2017 ===
 +Lösen Sie durch faktorisieren:
 +  - $x^2+4x+4 = 9$
 +  - $x^2-6x+9 = 4$
 +  - $x^2+8x+16 = 1$
 +
 +<hidden Lösungen>
 +  - $(x+2)^2 = 9$ also $(x+2)=\pm 3$, also $x_{1}=-5$, $x_=1$.
 +  - $(x-3)^2 = 4$ also $(x-3)=\pm 2$, also $x_1=1$, $x_2=5$.
 +  - $(x+4)^2 = 1$ also $(x+4)=\pm 1$, also $x_1=-5$, $x_2=3$.
 +</hidden>
 +=== Freitag 17. Februar 2017 ===
 +Lösen Sie schrittweise auf:
 +  - $${{15x}\over{8}}+{{4}\over{3}}={{7x}\over{4}}+{{13}\over{8}}$$
 +  - $${{19x}\over{20}}+{{6}\over{5}}={{4x}\over{5}}+{{7}\over{5}}$$
 +  - $${{53x}\over{18}}+{{7}\over{6}}={{8x}\over{3}}+{{4}\over{3}}$$
 +
 +
 +<hidden Lösungen>
 +1.
 +
 +$\begin{align*}
 +{{15x}\over{8}}+{{4}\over{3}} &= {{7x}\over{4}}+{{13}\over{8}} && |\cdot 24\\
 +45x+32 &= 42x+39 && |-\left(42x+32\right)\\
 +3x &= 7 && |:3\\
 +x &= {{7}\over{3}}
 +\end{align*}$
 +
 +2.
 +
 +$\begin{align*}
 +{{19x}\over{20}}+{{6}\over{5}} &= {{4x}\over{5}}+{{7}\over{5}} && |\cdot 20\\
 +19x+24 &= 16x+28 && |-\left(16x+24\right)\\
 +3x &= 4 && |:3\\
 +x &= {{4}\over{3}}
 +\end{align*}$
 +
 +3.
 +
 +$\begin{align*}
 +{{53x}\over{18}}+{{7}\over{6}} &= {{8x}\over{3}}+{{4}\over{3}} && |\cdot 18\\
 +53x+21 &= 48x+24 && |-\left(48x+21\right)\\
 +5x &= 3 && |:5\\
 +x &= {{3}\over{5}}
 +\end{align*}$
 +
 +</hidden>