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Beliebt Algebra >

16x^4-4x^2+1=0

Lösung

16 x^{4} - 4 x^{2} + 1 = 0

Lösung

x = \frac{3}{4} + \frac{1}{4} i, x = - \frac{3}{4} - \frac{1}{4} i, x = \frac{3}{4} - \frac{1}{4} i, x = - \frac{3}{4} + \frac{1}{4} i

Schritte zur Lösung

16 x^{4} - 4 x^{2} + 1 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

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

Löse

16 u^{2} - 4 u + 1 = 0 : u = \frac{1}{8} + i \frac{3}{8}, u = \frac{1}{8} - i \frac{3}{8}

u = \frac{1}{8} + i \frac{3}{8}, u = \frac{1}{8} - i \frac{3}{8}

Setze

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

löse für

x

Löse

x^{2} = \frac{1}{8} + i \frac{3}{8} : x = \frac{3}{4} + \frac{1}{4} i, x = - \frac{3}{4} - \frac{1}{4} i

Löse

x^{2} = \frac{1}{8} - i \frac{3}{8} : x = \frac{3}{4} - \frac{1}{4} i, x = - \frac{3}{4} + \frac{1}{4} i

Die Lösungen sind

x = \frac{3}{4} + \frac{1}{4} i, x = - \frac{3}{4} - \frac{1}{4} i, x = \frac{3}{4} - \frac{1}{4} i, x = - \frac{3}{4} + \frac{1}{4} i

Graph

Beliebte Beispiele

x^{10}+5x^5+6=0

x^{10} + 5 x^{5} + 6 = 0

solvefor y,x=y^{11}

so l v e f or y, x = y^{11}

0 = 36 x - x^{3}

z (z^{2} + 1) = 0

6 c^{5} + 4 c^{3} = 2