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Beliebt Algebra >

x^4-x^2+9=0

Lösung

x^{4} - x^{2} + 9 = 0

Lösung

x = \frac{7}{2} + \frac{5}{2} i, x = - \frac{7}{2} - \frac{5}{2} i, x = \frac{7}{2} - \frac{5}{2} i, x = - \frac{7}{2} + \frac{5}{2} i

Schritte zur Lösung

x^{4} - x^{2} + 9 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - u + 9 = 0

Löse

u^{2} - u + 9 = 0 : u = \frac{1}{2} + i \frac{35}{2}, u = \frac{1}{2} - i \frac{35}{2}

u = \frac{1}{2} + i \frac{35}{2}, u = \frac{1}{2} - i \frac{35}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{1}{2} + i \frac{35}{2} : x = \frac{7}{2} + \frac{5}{2} i, x = - \frac{7}{2} - \frac{5}{2} i

Löse

x^{2} = \frac{1}{2} - i \frac{35}{2} : x = \frac{7}{2} - \frac{5}{2} i, x = - \frac{7}{2} + \frac{5}{2} i

Die Lösungen sind

x = \frac{7}{2} + \frac{5}{2} i, x = - \frac{7}{2} - \frac{5}{2} i, x = \frac{7}{2} - \frac{5}{2} i, x = - \frac{7}{2} + \frac{5}{2} i

Graph

Beliebte Beispiele

(x^{2} + 5)^{2} = 0

x (2 x^{2} - 1) = 0

rationalrootstest 2x^3-11x^2+12x+9=0

r a t i o na l roo t s t es t 2 x^{3} - 11 x^{2} + 12 x + 9 = 0

4 x^{4} - 4 x = 0

4x-7x^5+16x^2=0

4 x - 7 x^{5} + 16 x^{2} = 0