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Beliebt Algebra >

x^8=10^{24}

Lösung

x^{8} = 1 0^{24}

Lösung

x = 1000, x = - 1000, x = 1000 i, x = - 1000 i, x = 5002 + 5002 i, x = - 5002 - 5002 i, x = 5002 - 5002 i, x = - 5002 + 5002 i

Schritte zur Lösung

x^{8} = 1 0^{24}

Schreibe die Gleichung um mit

u = x^{2}

und

u^{4} = x^{8}

u^{4} = 1 0^{24}

Löse

u^{4} = 1 0^{24} : u = 1000000, u = - 1000000, u = - 1 0^{12}, u = - - 1 0^{12}

u = 1000000, u = - 1000000, u = - 1 0^{12}, u = - - 1 0^{12}

Setze

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

löse für

x

Löse

x^{2} = 1000000 : x = 1000, x = - 1000

Löse

x^{2} = - 1000000 : x = 1000 i, x = - 1000 i

Löse

x^{2} = - 1 0^{12} : x = 5002 + 5002 i, x = - 5002 - 5002 i

Löse

x^{2} = - - 1 0^{12} : x = 5002 - 5002 i, x = - 5002 + 5002 i

Die Lösungen sind

x = 1000, x = - 1000, x = 1000 i, x = - 1000 i, x = 5002 + 5002 i, x = - 5002 - 5002 i, x = 5002 - 5002 i, x = - 5002 + 5002 i

Graph

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u^{4} u^{2} - 2 = 7 u

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5y^3-44y^2-9y=0

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