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Beliebt Algebra >

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

Lösung

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

Lösung

x = 2 2 + 3, x = - 2 2 + 3, x = 2 2 - 3, x = - 2 2 - 3

+1

Dezimale

x = 3.86370 \dots, x = - 3.86370 \dots, x = 1.03527 \dots, x = - 1.03527 \dots

Schritte zur Lösung

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

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

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

Löse

u^{2} - 16 u + 16 = 0 : u = 4 (2 + 3), u = 4 (2 - 3)

u = 4 (2 + 3), u = 4 (2 - 3)

Setze

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

löse für

x

Löse

x^{2} = 4 (2 + 3) : x = 2 2 + 3, x = - 2 2 + 3

Löse

x^{2} = 4 (2 - 3) : x = 2 2 - 3, x = - 2 2 - 3

Die Lösungen sind

x = 2 2 + 3, x = - 2 2 + 3, x = 2 2 - 3, x = - 2 2 - 3

Graph

Beliebte Beispiele

(x + 1)^{4} + 1 = 0

35 = (1 + x)^{4}

234514x^3-746760x+395221=0

234514 x^{3} - 746760 x + 395221 = 0

(r - 1)^{4} (r + 1) = 0

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