x^2+x+5=3sqrt(x^3+x^2-x+2)

Lösung

x^{2} + x + 5 = 3 x^{3} + x^{2} - x + 2

x \approx - 0.41421 \dots, x \approx - 1.14005 \dots, x \approx 2.41421 \dots, x \approx 6.14005 \dots

Schritte zur Lösung

x^{2} + x + 5 = 3 x^{3} + x^{2} - x + 2

Quadriere beide Seiten:

x^{4} + 2 x^{3} + 11 x^{2} + 10 x + 25 = 9 x^{3} + 9 x^{2} - 9 x + 18

x^{4} + 2 x^{3} + 11 x^{2} + 10 x + 25 = 9 x^{3} + 9 x^{2} - 9 x + 18

Löse

x^{4} + 2 x^{3} + 11 x^{2} + 10 x + 25 = 9 x^{3} + 9 x^{2} - 9 x + 18 : x \approx - 0.41421 \dots, x \approx - 1.14005 \dots, x \approx 2.41421 \dots, x \approx 6.14005 \dots

x \approx - 0.41421 \dots, x \approx - 1.14005 \dots, x \approx 2.41421 \dots, x \approx 6.14005 \dots

Überprüfe die Lösungen:

x \approx - 0.41421 \dots

Wahr

, x \approx - 1.14005 \dots

Wahr

, x \approx 2.41421 \dots

Wahr

, x \approx 6.14005 \dots

Wahr

Die Lösungen sind

x \approx - 0.41421 \dots, x \approx - 1.14005 \dots, x \approx 2.41421 \dots, x \approx 6.14005 \dots

x - 1 + 2 x - 2 = 2

256 16 + x = 16

- 4 x + 8 = 2 x

x - 2 = 4

x + 3 + x - 3 = 6