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Beliebt Algebra >

s^{16}=(16(-7+38))/2

Lösung

s^{16} = \frac{16 ( - 7 + 38 )}{2}

Lösung

s = 8248, s = - 8248, s = 8248 i, s = - 8248 i, s = \frac{16 31}{2 ^{\frac{5}{16}}} + \frac{4 4 31}{16 2 ^{5}} i, s = - \frac{8 31}{2 ^{\frac{5}{8}} 16 \frac{31}{2 ^{5}}} - \frac{4 4 31}{16 2 ^{5}} i, s = - \frac{16 31}{2 ^{\frac{5}{16}}} + \frac{4 4 31}{16 2 ^{5}} i, s = \frac{8 31}{2 ^{\frac{5}{8}} 16 \frac{31}{2 ^{5}}} - \frac{4 4 31}{16 2 ^{5}} i, s = \frac{8 31}{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2} + \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2}{2 8 2} i, s = - \frac{8 \frac{31}{2} 8 2}{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2} - \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2}{2 8 2} i, s = - \frac{8 31}{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2} + \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2}{2 8 2} i, s = \frac{8 \frac{31}{2} 8 2}{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2} - \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2}{2 8 2} i, s = \frac{8 31}{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2} + \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2}{2 8 2} i, s = - \frac{8 \frac{31}{2} 8 2}{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2} - \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2}{2 8 2} i, s = - \frac{8 31}{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2} + \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2}{2 8 2} i, s = \frac{8 \frac{31}{2} 8 2}{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2} - \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2}{2 8 2} i

Schritte zur Lösung

s^{16} = \frac{16 ( - 7 + 38 )}{2}

Vereinfache

\frac{16 ( - 7 + 38 )}{2} : 248

Schreibe die Gleichung um mit

u = s^{2}

und

u^{8} = s^{16}

u^{8} = 248

Löse

u^{8} = 248 : u = 4248, u = - 4248, u = 4248 i, u = - 4248 i, u = \frac{4 31}{2 ^{\frac{1}{4}} 8 \frac{31}{2}} + 4 \frac{31}{2} i, u = - \frac{4 31}{2 ^{\frac{1}{4}} 8 \frac{31}{2}} - 4 \frac{31}{2} i, u = - \frac{4 31}{2 ^{\frac{1}{4}} 8 \frac{31}{2}} + 4 \frac{31}{2} i, u = \frac{4 31}{2 ^{\frac{1}{4}} 8 \frac{31}{2}} - 4 \frac{31}{2} i

u = 4248, u = - 4248, u = 4248 i, u = - 4248 i, u = \frac{4 31}{2 ^{\frac{1}{4}} 8 \frac{31}{2}} + 4 \frac{31}{2} i, u = - \frac{4 31}{2 ^{\frac{1}{4}} 8 \frac{31}{2}} - 4 \frac{31}{2} i, u = - \frac{4 31}{2 ^{\frac{1}{4}} 8 \frac{31}{2}} + 4 \frac{31}{2} i, u = \frac{4 31}{2 ^{\frac{1}{4}} 8 \frac{31}{2}} - 4 \frac{31}{2} i

Setze

u = s^{2} w i e d er e in,

löse für

s

Löse

s^{2} = 4248 : s = 8248, s = - 8248

Löse

s^{2} = - 4248 : s = 8248 i, s = - 8248 i

Löse

s^{2} = 4248 i : s = \frac{16 31}{2 ^{\frac{5}{16}}} + \frac{4 4 31}{16 2 ^{5}} i, s = - \frac{8 31}{2 ^{\frac{5}{8}} 16 \frac{31}{2 ^{5}}} - \frac{4 4 31}{16 2 ^{5}} i

Löse

s^{2} = - 4248 i : s = - \frac{16 31}{2 ^{\frac{5}{16}}} + \frac{4 4 31}{16 2 ^{5}} i, s = \frac{8 31}{2 ^{\frac{5}{8}} 16 \frac{31}{2 ^{5}}} - \frac{4 4 31}{16 2 ^{5}} i

Löse

s^{2} = \frac{4 31}{2 ^{\frac{1}{4}} 8 \frac{31}{2}} + 4 \frac{31}{2} i : s = \frac{8 31}{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2} + \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2}{2 8 2} i, s = - \frac{8 \frac{31}{2} 8 2}{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2} - \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2}{2 8 2} i

Löse

s^{2} = - \frac{4 31}{2 ^{\frac{1}{4}} 8 \frac{31}{2}} - 4 \frac{31}{2} i : s = - \frac{8 31}{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2} + \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2}{2 8 2} i, s = \frac{8 \frac{31}{2} 8 2}{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2} - \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2}{2 8 2} i

Löse

s^{2} = - \frac{4 31}{2 ^{\frac{1}{4}} 8 \frac{31}{2}} + 4 \frac{31}{2} i : s = \frac{8 31}{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2} + \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2}{2 8 2} i, s = - \frac{8 \frac{31}{2} 8 2}{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2} - \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2}{2 8 2} i

Löse

s^{2} = \frac{4 31}{2 ^{\frac{1}{4}} 8 \frac{31}{2}} - 4 \frac{31}{2} i : s = - \frac{8 31}{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2} + \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2}{2 8 2} i, s = \frac{8 \frac{31}{2} 8 2}{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2} - \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2}{2 8 2} i

Die Lösungen sind

s = 8248, s = - 8248, s = 8248 i, s = - 8248 i, s = \frac{16 31}{2 ^{\frac{5}{16}}} + \frac{4 4 31}{16 2 ^{5}} i, s = - \frac{8 31}{2 ^{\frac{5}{8}} 16 \frac{31}{2 ^{5}}} - \frac{4 4 31}{16 2 ^{5}} i, s = - \frac{16 31}{2 ^{\frac{5}{16}}} + \frac{4 4 31}{16 2 ^{5}} i, s = \frac{8 31}{2 ^{\frac{5}{8}} 16 \frac{31}{2 ^{5}}} - \frac{4 4 31}{16 2 ^{5}} i, s = \frac{8 31}{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2} + \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2}{2 8 2} i, s = - \frac{8 \frac{31}{2} 8 2}{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2} - \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2}{2 8 2} i, s = - \frac{8 31}{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2} + \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2}{2 8 2} i, s = \frac{8 \frac{31}{2} 8 2}{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2} - \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2}{2 8 2} i, s = \frac{8 31}{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2} + \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2}{2 8 2} i, s = - \frac{8 \frac{31}{2} 8 2}{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2} - \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 + 8 3968 4 2}{2 8 2} i, s = - \frac{8 31}{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2} + \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2}{2 8 2} i, s = \frac{8 \frac{31}{2} 8 2}{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2} - \frac{2 ^{\frac{5}{8}} \cdot 2 8 31 - 8 3968 4 2}{2 8 2} i

Graph

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