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Beliebt Algebra >

25x^4-20x^2+3=0

Lösung

25 x^{4} - 20 x^{2} + 3 = 0

Lösung

x = \frac{3}{5}, x = - \frac{3}{5}, x = \frac{1}{5}, x = - \frac{1}{5}

+1

Dezimale

x = 0.77459 \dots, x = - 0.77459 \dots, x = 0.4472135955, x = - 0.4472135955

Schritte zur Lösung

25 x^{4} - 20 x^{2} + 3 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

25 u^{2} - 20 u + 3 = 0

Löse

25 u^{2} - 20 u + 3 = 0 : u = \frac{3}{5}, u = \frac{1}{5}

u = \frac{3}{5}, u = \frac{1}{5}

Setze

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

löse für

x

Löse

x^{2} = \frac{3}{5} : x = \frac{3}{5}, x = - \frac{3}{5}

Löse

x^{2} = \frac{1}{5} : x = \frac{1}{5}, x = - \frac{1}{5}

Die Lösungen sind

x = \frac{3}{5}, x = - \frac{3}{5}, x = \frac{1}{5}, x = - \frac{1}{5}

Graph

Beliebte Beispiele

x^{3} - 5 x^{2} - 6 x = 0

x^3+5x^2+3x-9=0

x^{3} + 5 x^{2} + 3 x - 9 = 0

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

(x^{2} - 9)^{2} = 0

8x^3+x^2-2x-1=0

8 x^{3} + x^{2} - 2 x - 1 = 0