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# solve(256+(1/4x)^2=(1/2x)^2) Wie ist das ohne Taschenrechner zu lösen?

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solve(256+(1/4x)^2=(1/2x)^2)

Wie ist das ohne Taschenrechner zu lösen?

01.07.2015

#1
+14538
+3

### Guten Morgen Anonymous,

$${\mathtt{256}}{\mathtt{\,\small\textbf+\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}{\mathtt{\,\times\,}}{\mathtt{x}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}{\mathtt{\,\times\,}}{\mathtt{x}}\right) = \left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\mathtt{x}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)$$

$${\mathtt{256}}{\mathtt{\,\small\textbf+\,}}{\frac{{{\mathtt{x}}}^{{\mathtt{2}}}}{{\mathtt{16}}}} = {\frac{{{\mathtt{x}}}^{{\mathtt{2}}}}{{\mathtt{4}}}}$$                          $${\frac{{{\mathtt{x}}}^{{\mathtt{2}}}}{{\mathtt{4}}}} = {\frac{{\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}}{{\mathtt{16}}}}$$

$${\mathtt{256}} = {\frac{{\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}}{{\mathtt{16}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}}{{\mathtt{16}}}}$$

$${\mathtt{256}} = {\frac{{\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{3}}}}{{\mathtt{16}}}}$$          =>       $${{\mathtt{x}}}^{{\mathtt{2}}} = {\frac{{\mathtt{256}}{\mathtt{\,\times\,}}{\mathtt{16}}}{{\mathtt{3}}}}$$          ;   $${\mathtt{256}}{\mathtt{\,\times\,}}{\mathtt{16}} = {{\mathtt{2}}}^{{\mathtt{8}}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{4}}} = {{\mathtt{2}}}^{{\mathtt{12}}}$$

01.07.2015

#1
+14538
+3
Beste Antwort

### Guten Morgen Anonymous,

$${\mathtt{256}}{\mathtt{\,\small\textbf+\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}{\mathtt{\,\times\,}}{\mathtt{x}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}{\mathtt{\,\times\,}}{\mathtt{x}}\right) = \left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\mathtt{x}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)$$

$${\mathtt{256}}{\mathtt{\,\small\textbf+\,}}{\frac{{{\mathtt{x}}}^{{\mathtt{2}}}}{{\mathtt{16}}}} = {\frac{{{\mathtt{x}}}^{{\mathtt{2}}}}{{\mathtt{4}}}}$$                          $${\frac{{{\mathtt{x}}}^{{\mathtt{2}}}}{{\mathtt{4}}}} = {\frac{{\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}}{{\mathtt{16}}}}$$

$${\mathtt{256}} = {\frac{{\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}}{{\mathtt{16}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}}{{\mathtt{16}}}}$$

$${\mathtt{256}} = {\frac{{\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{3}}}}{{\mathtt{16}}}}$$          =>       $${{\mathtt{x}}}^{{\mathtt{2}}} = {\frac{{\mathtt{256}}{\mathtt{\,\times\,}}{\mathtt{16}}}{{\mathtt{3}}}}$$          ;   $${\mathtt{256}}{\mathtt{\,\times\,}}{\mathtt{16}} = {{\mathtt{2}}}^{{\mathtt{8}}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{4}}} = {{\mathtt{2}}}^{{\mathtt{12}}}$$