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Beliebt Algebra >

a^8-47a^4+1=0

Lösung

a^{8} - 47 a^{4} + 1 = 0

Lösung

a = 4 \frac{47 + 21 5}{2}, a = - 4 \frac{47 + 21 5}{2}, a = i 4 \frac{47 + 21 5}{2}, a = - i 4 \frac{47 + 21 5}{2}, a = 4 \frac{47 - 21 5}{2}, a = - 4 \frac{47 - 21 5}{2}, a = i 4 \frac{47 - 21 5}{2}, a = - i 4 \frac{47 - 21 5}{2}

Schritte zur Lösung

a^{8} - 47 a^{4} + 1 = 0

Schreibe die Gleichung um mit

u = a^{2}, u^{2} = a^{4}

und

u^{4} = a^{8}

u^{4} - 47 u^{2} + 1 = 0

Löse

u^{4} - 47 u^{2} + 1 = 0 : u = \frac{47 + 21 5}{2}, u = - \frac{47 + 21 5}{2}, u = \frac{47 - 21 5}{2}, u = - \frac{47 - 21 5}{2}

u = \frac{47 + 21 5}{2}, u = - \frac{47 + 21 5}{2}, u = \frac{47 - 21 5}{2}, u = - \frac{47 - 21 5}{2}

Setze

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

löse für

a

Löse

a^{2} = \frac{47 + 21 5}{2} : a = 4 \frac{47 + 21 5}{2}, a = - 4 \frac{47 + 21 5}{2}

Löse

a^{2} = - \frac{47 + 21 5}{2} : a = i 4 \frac{47 + 21 5}{2}, a = - i 4 \frac{47 + 21 5}{2}

Löse

a^{2} = \frac{47 - 21 5}{2} : a = 4 \frac{47 - 21 5}{2}, a = - 4 \frac{47 - 21 5}{2}

Löse

a^{2} = - \frac{47 - 21 5}{2} : a = i 4 \frac{47 - 21 5}{2}, a = - i 4 \frac{47 - 21 5}{2}

Die Lösungen sind

a = 4 \frac{47 + 21 5}{2}, a = - 4 \frac{47 + 21 5}{2}, a = i 4 \frac{47 + 21 5}{2}, a = - i 4 \frac{47 + 21 5}{2}, a = 4 \frac{47 - 21 5}{2}, a = - 4 \frac{47 - 21 5}{2}, a = i 4 \frac{47 - 21 5}{2}, a = - i 4 \frac{47 - 21 5}{2}

Graph

Beliebte Beispiele

(2x+1)^8=5.9^7+4.9^7

(2 x + 1)^{8} = 5. 9^{7} + 4. 9^{7}

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x^{1} + 2 x^{2} - x^{3} = 4

3x^3-10x^2+8x=0

3 x^{3} - 10 x^{2} + 8 x = 0