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Beliebt Algebra >

solvefor x,x^6= 9/4

Lösung

löse nach

x, x^{6} = \frac{9}{4}

Lösung

x = 3 \frac{9}{4}, x = - 3 \frac{9}{4}, x = 0.57235 \dots + 0.99135 \dots i, x = - 0.57235 \dots - 0.99135 \dots i, x = 0.57235 \dots - 0.99135 \dots i, x = - 0.57235 \dots + 0.99135 \dots i

Schritte zur Lösung

x^{6} = \frac{9}{4}

Schreibe die Gleichung um mit

u = x^{2}

und

u^{3} = x^{6}

u^{3} = \frac{9}{4}

Löse

u^{3} = \frac{9}{4} : u = 3 \frac{9}{4}, u = 3 \frac{9}{4} \frac{- 1 + 3 i}{2}, u = 3 \frac{9}{4} \frac{- 1 - 3 i}{2}

u = 3 \frac{9}{4}, u = 3 \frac{9}{4} \frac{- 1 + 3 i}{2}, u = 3 \frac{9}{4} \frac{- 1 - 3 i}{2}

Setze

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

löse für

x

Löse

x^{2} = 3 \frac{9}{4} : x = 3 \frac{9}{4}, x = - 3 \frac{9}{4}

Löse

x^{2} = 3 \frac{9}{4} \frac{- 1 + 3 i}{2} : x = 0.57235 \dots + 0.99135 \dots i, x = - 0.57235 \dots - 0.99135 \dots i

Löse

x^{2} = 3 \frac{9}{4} \frac{- 1 - 3 i}{2} : x = 0.57235 \dots - 0.99135 \dots i, x = - 0.57235 \dots + 0.99135 \dots i

Die Lösungen sind

x = 3 \frac{9}{4}, x = - 3 \frac{9}{4}, x = 0.57235 \dots + 0.99135 \dots i, x = - 0.57235 \dots - 0.99135 \dots i, x = 0.57235 \dots - 0.99135 \dots i, x = - 0.57235 \dots + 0.99135 \dots i

Graph

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