36x^4-83x^2+35=0

Lösung

36 x^{4} - 83 x^{2} + 35 = 0

x = \frac{7}{2}, x = - \frac{7}{2}, x = \frac{5}{3}, x = - \frac{5}{3}

Dezimale

x = 1.32287 \dots, x = - 1.32287 \dots, x = 0.74535 \dots, x = - 0.74535 \dots

Schritte zur Lösung

36 x^{4} - 83 x^{2} + 35 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

36 u^{2} - 83 u + 35 = 0

Löse

36 u^{2} - 83 u + 35 = 0 : u = \frac{7}{4}, u = \frac{5}{9}

u = \frac{7}{4}, u = \frac{5}{9}

Setze

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

löse für

x

Löse

x^{2} = \frac{7}{4} : x = \frac{7}{2}, x = - \frac{7}{2}

Löse

x^{2} = \frac{5}{9} : x = \frac{5}{3}, x = - \frac{5}{3}

Die Lösungen sind

x = \frac{7}{2}, x = - \frac{7}{2}, x = \frac{5}{3}, x = - \frac{5}{3}

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

(6 x^{3}) x^{5} = 6 x (3 x^{5})

x^{3} - 2 x^{2} - 2 x - 1 = - 3

(x^{2} + 4)^{2} - 11 (x^{2} + 4) + 24 = 0

3 x^{3} - 4 x^{2} + 11 x + 10 = 0