x^2-6x=13sqrt(x^2-6x-36)

Lösung

x^{2} - 6 x = 13 x^{2} - 6 x - 36

x \approx - 4.81024 \dots, x \approx 10.81024 \dots, x \approx - 8.22497 \dots, x \approx 14.22497 \dots

Schritte zur Lösung

x^{2} - 6 x = 13 x^{2} - 6 x - 36

Quadriere beide Seiten:

x^{4} - 12 x^{3} + 36 x^{2} = 169 x^{2} - 1014 x - 6084

x^{4} - 12 x^{3} + 36 x^{2} = 169 x^{2} - 1014 x - 6084

Löse

x^{4} - 12 x^{3} + 36 x^{2} = 169 x^{2} - 1014 x - 6084 : x \approx - 4.81024 \dots, x \approx 10.81024 \dots, x \approx - 8.22497 \dots, x \approx 14.22497 \dots

x \approx - 4.81024 \dots, x \approx 10.81024 \dots, x \approx - 8.22497 \dots, x \approx 14.22497 \dots

Überprüfe die Lösungen:

x \approx - 4.81024 \dots

Wahr

, x \approx 10.81024 \dots

Wahr

, x \approx - 8.22497 \dots

Wahr

, x \approx 14.22497 \dots

Wahr

Die Lösungen sind

x \approx - 4.81024 \dots, x \approx 10.81024 \dots, x \approx - 8.22497 \dots, x \approx 14.22497 \dots

6 x - 18 x - 8 = 2

x + 2 + x = 2

x = 1 - x

(5 x + 1)^{\frac{1}{2}} = 6

3 2 x + 7 + x + 3 = 11