=(18a+- Wurzel aus 252*a^2)/(18*a^2) Was darf ich davon wegkürzen

Hallo anonymous!

u1= (18a ±sqrt (252*a^2))/(18*a^2)

u1 = (18a ±√(252a²)) / 18a²

u1 = (18a ±√(7 * 36a²)) / 18a²

u1 = (18a ± 6a * √ 7) / 18a²         kürzen durch 6a

u1 = (3 ±√ 7) / 3a

oder etwas ausführlicher

u1 = (2 * 3 * 3a ± √(2 * 2 * 3 * 3 *7a²)) / (2 * 3 * 3a²)

u1 = (2 * 3 * 3a ± 2 * 3a * √ 7) / (2 * 3 * 3a²)        durch 2 * 3a kürzen

u1 =(2 * 3a) * (3 ± √ 7) / ((2 * 3a) * 3a)

u1 =(3 ± √ 7) / 3a

Gruß  :- )                           P.S.: Ich habe das ± noch nachträglich eingesetzt.

$${\mathtt{u1}} = {\frac{\left({\mathtt{18}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{252}}{\mathtt{\,\times\,}}{{\mathtt{a}}}^{{\mathtt{2}}}}}\right)}{\left({\mathtt{18}}{\mathtt{\,\times\,}}{{\mathtt{a}}}^{{\mathtt{2}}}\right)}}$$

$${\mathtt{u1}} = {\frac{\left({\mathtt{18}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{36}}{\mathtt{\,\times\,}}{{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{7}}}}\right)}{\left({\mathtt{18}}{\mathtt{\,\times\,}}{{\mathtt{a}}}^{{\mathtt{2}}}\right)}}$$

$${\mathtt{u1}} = {\frac{\left[{\mathtt{18}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,-\,}}\left({\mathtt{6}}{\mathtt{\,\times\,}}{\left|{\mathtt{a}}\right|}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{7}}}}\right)\right]}{\left({\mathtt{18}}{\mathtt{\,\times\,}}{{\mathtt{a}}}^{{\mathtt{2}}}\right)}}$$

$${\mathtt{u1}} = {\frac{\left[{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,-\,}}\left({\left|{\mathtt{a}}\right|}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{7}}}}\right)\right]}{\left({\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{a}}}^{{\mathtt{2}}}\right)}}$$

Ergänzung: (Danke Radix) Ich hätte das abs(a) und a nicht zusammen gefasst...

$${\mathtt{u1}} = {\frac{{\mathtt{a}}{\mathtt{\,\times\,}}\left({\mathtt{3}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{7}}}}\right)}{\left({\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{a}}}^{{\mathtt{2}}}\right)}}$$

$${\mathtt{u1}} = {\frac{\left({\mathtt{3}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{7}}}}\right)}{\left({\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{a}}\right)}}$$

Guten Morgen Anonymous 2,

du kannst im Zähler noch  a  ausklammern und gegen ein  a  im Nenner kürzen.

Im Zähler darf auch ein + Zeichen stehen. ( siehe  asinus ! )

Gruß radix !