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Beliebt Algebra >

d^{16}-d^8+8d+13=8d+19

Lösung

d^{16} - d^{8} + 8 d + 13 = 8 d + 19

Lösung

d = 43, d = - 43, d = 43 i, d = - 43 i, d = \frac{8 3}{2} + \frac{4 3}{2} i, d = - \frac{8 3}{2} - \frac{4 3}{2} i, d = - \frac{8 3}{2} + \frac{4 3}{2} i, d = \frac{8 3}{2} - \frac{4 3}{2} i, d = \frac{1}{2 ^{\frac{5}{8}} 2 - 1} + \frac{2 - 1}{2 ^{\frac{5}{8}}} i, d = - \frac{1}{2 ^{\frac{5}{4}} \cdot \frac{2 - 1}{2 ^{\frac{5}{8}}}} - \frac{2 - 1}{2 ^{\frac{5}{8}}} i, d = - \frac{1}{2 ^{\frac{5}{8}} 1 + 2} + \frac{1 + 2}{2 ^{\frac{5}{8}}} i, d = \frac{1}{2 ^{\frac{5}{8}} 1 + 2} - \frac{1 + 2}{2 ^{\frac{5}{8}}} i, d = \frac{1}{2 ^{\frac{5}{8}} 1 + 2} + \frac{1 + 2}{2 ^{\frac{5}{8}}} i, d = - \frac{1}{2 ^{\frac{5}{4}} \cdot \frac{1 + 2}{2 ^{\frac{5}{8}}}} - \frac{1 + 2}{2 ^{\frac{5}{8}}} i, d = - \frac{1}{2 ^{\frac{5}{8}} 2 - 1} + \frac{2 - 1}{2 ^{\frac{5}{8}}} i, d = \frac{1}{2 ^{\frac{5}{8}} 2 - 1} - \frac{2 - 1}{2 ^{\frac{5}{8}}} i

Schritte zur Lösung

d^{16} - d^{8} + 8 d + 13 = 8 d + 19

Verschiebe

19

auf die linke Seite

d^{16} - d^{8} + 8 d - 6 = 8 d

Verschiebe

8 d

auf die linke Seite

d^{16} - d^{8} - 6 = 0

Schreibe die Gleichung um mit

u = d^{2}, u^{4} = d^{8}

und

u^{8} = d^{16}

u^{8} - u^{4} - 6 = 0

Löse

u^{8} - u^{4} - 6 = 0 : u = 3, u = - 3, u = 3 i, u = - 3 i, u = \frac{1}{2 ^{\frac{1}{4}}} + \frac{1}{4 2} i, u = - \frac{1}{4 2} - \frac{1}{4 2} i, u = - \frac{1}{2 ^{\frac{1}{4}}} + \frac{1}{4 2} i, u = \frac{1}{4 2} - \frac{1}{4 2} i

u = 3, u = - 3, u = 3 i, u = - 3 i, u = \frac{1}{2 ^{\frac{1}{4}}} + \frac{1}{4 2} i, u = - \frac{1}{4 2} - \frac{1}{4 2} i, u = - \frac{1}{2 ^{\frac{1}{4}}} + \frac{1}{4 2} i, u = \frac{1}{4 2} - \frac{1}{4 2} i

Setze

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

löse für

d

Löse

d^{2} = 3 : d = 43, d = - 43

Löse

d^{2} = - 3 : d = 43 i, d = - 43 i

Löse

d^{2} = 3 i : d = \frac{8 3}{2} + \frac{4 3}{2} i, d = - \frac{8 3}{2} - \frac{4 3}{2} i

Löse

d^{2} = - 3 i : d = - \frac{8 3}{2} + \frac{4 3}{2} i, d = \frac{8 3}{2} - \frac{4 3}{2} i

Löse

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

Löse

d^{2} = - \frac{1}{4 2} - \frac{1}{4 2} i : d = - \frac{1}{2 ^{\frac{5}{8}} 1 + 2} + \frac{1 + 2}{2 ^{\frac{5}{8}}} i, d = \frac{1}{2 ^{\frac{5}{8}} 1 + 2} - \frac{1 + 2}{2 ^{\frac{5}{8}}} i

Löse

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

Löse

d^{2} = \frac{1}{4 2} - \frac{1}{4 2} i : d = - \frac{1}{2 ^{\frac{5}{8}} 2 - 1} + \frac{2 - 1}{2 ^{\frac{5}{8}}} i, d = \frac{1}{2 ^{\frac{5}{8}} 2 - 1} - \frac{2 - 1}{2 ^{\frac{5}{8}}} i

Die Lösungen sind

d = 43, d = - 43, d = 43 i, d = - 43 i, d = \frac{8 3}{2} + \frac{4 3}{2} i, d = - \frac{8 3}{2} - \frac{4 3}{2} i, d = - \frac{8 3}{2} + \frac{4 3}{2} i, d = \frac{8 3}{2} - \frac{4 3}{2} i, d = \frac{1}{2 ^{\frac{5}{8}} 2 - 1} + \frac{2 - 1}{2 ^{\frac{5}{8}}} i, d = - \frac{1}{2 ^{\frac{5}{4}} \cdot \frac{2 - 1}{2 ^{\frac{5}{8}}}} - \frac{2 - 1}{2 ^{\frac{5}{8}}} i, d = - \frac{1}{2 ^{\frac{5}{8}} 1 + 2} + \frac{1 + 2}{2 ^{\frac{5}{8}}} i, d = \frac{1}{2 ^{\frac{5}{8}} 1 + 2} - \frac{1 + 2}{2 ^{\frac{5}{8}}} i, d = \frac{1}{2 ^{\frac{5}{8}} 1 + 2} + \frac{1 + 2}{2 ^{\frac{5}{8}}} i, d = - \frac{1}{2 ^{\frac{5}{4}} \cdot \frac{1 + 2}{2 ^{\frac{5}{8}}}} - \frac{1 + 2}{2 ^{\frac{5}{8}}} i, d = - \frac{1}{2 ^{\frac{5}{8}} 2 - 1} + \frac{2 - 1}{2 ^{\frac{5}{8}}} i, d = \frac{1}{2 ^{\frac{5}{8}} 2 - 1} - \frac{2 - 1}{2 ^{\frac{5}{8}}} i

Graph

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