9x^4-148x^2+64=0

Lösung

9 x^{4} - 148 x^{2} + 64 = 0

x = 4, x = - 4, x = \frac{2}{3}, x = - \frac{2}{3}

Dezimale

x = 4, x = - 4, x = 0.66666 \dots, x = - 0.66666 \dots

Schritte zur Lösung

9 x^{4} - 148 x^{2} + 64 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

9 u^{2} - 148 u + 64 = 0

Löse

9 u^{2} - 148 u + 64 = 0 : u = 16, u = \frac{4}{9}

u = 16, u = \frac{4}{9}

Setze

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

löse für

x

Löse

x^{2} = 16 : x = 4, x = - 4

Löse

x^{2} = \frac{4}{9} : x = \frac{2}{3}, x = - \frac{2}{3}

Die Lösungen sind

x = 4, x = - 4, x = \frac{2}{3}, x = - \frac{2}{3}

x^{3} - 25 x^{2} + 156.25 x = 50

2 x^{4} = 24 x^{2}

6 x^{4} + 13 x^{3} - 8 x^{2} - 17 x + 6 = 0

so l v e f or y, y^{2} = x^{2} - x^{4}

roo t s x^{3} + 5 x^{2} + 9 x + 5