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Beliebt Algebra >

4x^4-9x^2+3=0

Lösung

4 x^{4} - 9 x^{2} + 3 = 0

Lösung

x = \frac{9 + 33}{2 2}, x = - \frac{9 + 33}{2 2}, x = \frac{9 - 33}{2 2}, x = - \frac{9 - 33}{2 2}

+1

Dezimale

x = 1.35759 \dots, x = - 1.35759 \dots, x = 0.63791 \dots, x = - 0.63791 \dots

Schritte zur Lösung

4 x^{4} - 9 x^{2} + 3 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

4 u^{2} - 9 u + 3 = 0

Löse

4 u^{2} - 9 u + 3 = 0 : u = \frac{9 + 33}{8}, u = \frac{9 - 33}{8}

u = \frac{9 + 33}{8}, u = \frac{9 - 33}{8}

Setze

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

löse für

x

Löse

x^{2} = \frac{9 + 33}{8} : x = \frac{9 + 33}{2 2}, x = - \frac{9 + 33}{2 2}

Löse

x^{2} = \frac{9 - 33}{8} : x = \frac{9 - 33}{2 2}, x = - \frac{9 - 33}{2 2}

Die Lösungen sind

x = \frac{9 + 33}{2 2}, x = - \frac{9 + 33}{2 2}, x = \frac{9 - 33}{2 2}, x = - \frac{9 - 33}{2 2}

Graph

Beliebte Beispiele

y^4-10y^3+5y^2+100y+100=0

y^{4} - 10 y^{3} + 5 y^{2} + 100 y + 100 = 0

x^{4} = 45 x + 76

x + x^{2} + x^{4} = 2000

x^{3} + x + 3 = 0

3 x^{4} - 8 x^{2} - 4 = 0