(x^2-5x-28)^{4/3}=16

Lösung

(x^{2} - 5 x - 28)^{\frac{4}{3}} = 16

x = 9, x = - 4, x = \frac{5 + 10 5 ^{\frac{1}{2}}}{2}, x = \frac{5 - 10 5 ^{\frac{1}{2}}}{2}

Dezimale

x = 9, x = - 4, x = 7.62347 \dots, x = - 2.62347 \dots

Schritte zur Lösung

(x^{2} - 5 x - 28)^{\frac{4}{3}} = 16

Potenziere beide Seiten der Gleichung mit

3 : (x^{2} - 5 x - 28)^{4} = 4096

(x^{2} - 5 x - 28)^{4} = 4096

Löse

(x^{2} - 5 x - 28)^{4} = 4096 : x = 9, x = - 4, x = \frac{5 + 10 5 ^{\frac{1}{2}}}{2}, x = \frac{5 - 10 5 ^{\frac{1}{2}}}{2}

x = 9, x = - 4, x = \frac{5 + 10 5 ^{\frac{1}{2}}}{2}, x = \frac{5 - 10 5 ^{\frac{1}{2}}}{2}

Überprüfe die Lösungen:

x = 9

Wahr

, x = - 4

Wahr

, x = \frac{5 + 10 5 ^{\frac{1}{2}}}{2}

Wahr

, x = \frac{5 - 10 5 ^{\frac{1}{2}}}{2}

Wahr

Die Lösungen sind

x = 9, x = - 4, x = \frac{5 + 10 5 ^{\frac{1}{2}}}{2}, x = \frac{5 - 10 5 ^{\frac{1}{2}}}{2}

x^{2} - 5 = 1 + x^{2}

2 x - \frac{54}{x} = 0

3 y + 37 + 7 = y + 6

y = y - 6

x + 1 = 1 - x