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Beliebt Algebra >

x^4-6x^2+7=0

Lösung

x^{4} - 6 x^{2} + 7 = 0

Lösung

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

+1

Dezimale

x = 2.10100 \dots, x = - 2.10100 \dots, x = 1.25928 \dots, x = - 1.25928 \dots

Schritte zur Lösung

x^{4} - 6 x^{2} + 7 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - 6 u + 7 = 0

Löse

u^{2} - 6 u + 7 = 0 : u = 3 + 2, u = 3 - 2

u = 3 + 2, u = 3 - 2

Setze

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

löse für

x

Löse

x^{2} = 3 + 2 : x = 3 + 2, x = - 3 + 2

Löse

x^{2} = 3 - 2 : x = 3 - 2, x = - 3 - 2

Die Lösungen sind

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

Graph

Beliebte Beispiele

3(x^2-49)(36x^2-49)=0

3 (x^{2} - 49) (36 x^{2} - 49) = 0

9x^4-40x^2+16=0

9 x^{4} - 40 x^{2} + 16 = 0

x^4-2x^3+6x-1=0

x^{4} - 2 x^{3} + 6 x - 1 = 0

125 x^{3} - 27 = 0

2x^3-x^2-7x+6=0

2 x^{3} - x^{2} - 7 x + 6 = 0