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Beliebt Algebra >

x^7x=238

Lösung

x^{7} x = 238

Lösung

x = 4238, x = - 4238, x = 4238 i, x = - 4238 i, x = \frac{4 119}{8 2 ^{3}} + \frac{8 119}{8 2 ^{3}} i, x = - \frac{4 119}{8 2 ^{3}} - \frac{8 119}{8 2 ^{3}} i, x = \frac{4 119}{8 2 ^{3}} - \frac{8 119}{8 2 ^{3}} i, x = - \frac{4 119}{8 2 ^{3}} + \frac{8 119}{8 2 ^{3}} i

Schritte zur Lösung

x^{7} x = 238

Vereinfache

x^{8} = 238

Schreibe die Gleichung um mit

u = x^{2}

und

u^{4} = x^{8}

u^{4} = 238

Löse

u^{4} = 238 : u = 238, u = - 238, u = 238 i, u = - 238 i

u = 238, u = - 238, u = 238 i, u = - 238 i

Setze

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

löse für

x

Löse

x^{2} = 238 : x = 4238, x = - 4238

Löse

x^{2} = - 238 : x = 4238 i, x = - 4238 i

Löse

x^{2} = 238 i : x = \frac{4 119}{8 2 ^{3}} + \frac{8 119}{8 2 ^{3}} i, x = - \frac{4 119}{8 2 ^{3}} - \frac{8 119}{8 2 ^{3}} i

Löse

x^{2} = - 238 i : x = \frac{4 119}{8 2 ^{3}} - \frac{8 119}{8 2 ^{3}} i, x = - \frac{4 119}{8 2 ^{3}} + \frac{8 119}{8 2 ^{3}} i

Die Lösungen sind

x = 4238, x = - 4238, x = 4238 i, x = - 4238 i, x = \frac{4 119}{8 2 ^{3}} + \frac{8 119}{8 2 ^{3}} i, x = - \frac{4 119}{8 2 ^{3}} - \frac{8 119}{8 2 ^{3}} i, x = \frac{4 119}{8 2 ^{3}} - \frac{8 119}{8 2 ^{3}} i, x = - \frac{4 119}{8 2 ^{3}} + \frac{8 119}{8 2 ^{3}} i

Graph

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