x^4-(sqrt(5)+sqrt(2))*x^2+sqrt(10)=0

Lösung

x^{4} - (5 + 2) \cdot x^{2} + 10 = 0

x = \frac{5 + 2 + 7 - 2 10}{2}, x = - \frac{5 + 2 + 7 - 2 10}{2}, x = \frac{5 + 2 - 7 - 2 10}{2}, x = - \frac{5 + 2 - 7 - 2 10}{2}

Dezimale

x = 1.49534 \dots, x = - 1.49534 \dots, x = 1.18920 \dots, x = - 1.18920 \dots

Schritte zur Lösung

x^{4} - (5 + 2) x^{2} + 10 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - (5 + 2) u + 10 = 0

Löse

u^{2} - (5 + 2) u + 10 = 0 : u = \frac{5 + 2 + 7 - 2 10}{2}, u = \frac{5 + 2 - 7 - 2 10}{2}

u = \frac{5 + 2 + 7 - 2 10}{2}, u = \frac{5 + 2 - 7 - 2 10}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{5 + 2 + 7 - 2 10}{2} : x = \frac{5 + 2 + 7 - 2 10}{2}, x = - \frac{5 + 2 + 7 - 2 10}{2}

Löse

x^{2} = \frac{5 + 2 - 7 - 2 10}{2} : x = \frac{5 + 2 - 7 - 2 10}{2}, x = - \frac{5 + 2 - 7 - 2 10}{2}

Die Lösungen sind

x = \frac{5 + 2 + 7 - 2 10}{2}, x = - \frac{5 + 2 + 7 - 2 10}{2}, x = \frac{5 + 2 - 7 - 2 10}{2}, x = - \frac{5 + 2 - 7 - 2 10}{2}

(x^{2} + x - 6) (x^{2} - 3 x - 4) = 24

so l v e f or x, (3 x + 7)^{5} = 2 y^{3}

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

(x + 2)^{3} = 2 x (x^{2} - 1)

x^{3} + 2 x - 12 = 0