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x^{23}x-4+4x=10+x^2

Lösung

x^{23} x - 4 + 4 x = 10 + x^{2}

x \approx 1.10423 \dots, x \approx - 1.13250 \dots

Schritte zur Lösung

x^{23} x - 4 + 4 x = 10 + x^{2}

Schreibe

x^{23} x - 4 + 4 x

um:

x^{24} - 4 + 4 x

x^{24} - 4 + 4 x = 10 + x^{2}

Verschiebe

x^{2}

auf die linke Seite

x^{24} - 4 + 4 x - x^{2} = 10

Verschiebe

10

auf die linke Seite

x^{24} - x^{2} + 4 x - 14 = 0

Bestimme eine Lösung für

x^{24} - x^{2} + 4 x - 14 = 0

nach dem Newton-Raphson-Verfahren:

x \approx 1.10423 \dots

Wende die schriftliche Division an:

\frac{x ^{24} - x ^{2} + 4 x - 14}{x - 1.10423 \dots} = x^{23} + 1.10423 \dots x^{22} + 1.21934 \dots x^{21} + 1.34644 \dots x^{20} + 1.48680 \dots x^{19} + 1.64178 \dots x^{18} + 1.81292 \dots x^{17} + 2.00190 \dots x^{16} + 2.21058 \dots x^{15} + 2.44101 \dots x^{14} + 2.69546 \dots x^{13} + 2.97643 \dots x^{12} + 3.28669 \dots x^{11} + 3.62930 \dots x^{10} + 4.00761 \dots x^{9} + 4.42537 \dots x^{8} + 4.88667 \dots x^{7} + 5.39605 \dots x^{6} + 5.95853 \dots x^{5} + 6.57965 \dots x^{4} + 7.26551 \dots x^{3} + 8.02286 \dots x^{2} + 7.85917 \dots x + 12.67840 \dots

x^{23} + 1.10423 \dots x^{22} + 1.21934 \dots x^{21} + 1.34644 \dots x^{20} + 1.48680 \dots x^{19} + 1.64178 \dots x^{18} + 1.81292 \dots x^{17} + 2.00190 \dots x^{16} + 2.21058 \dots x^{15} + 2.44101 \dots x^{14} + 2.69546 \dots x^{13} + 2.97643 \dots x^{12} + 3.28669 \dots x^{11} + 3.62930 \dots x^{10} + 4.00761 \dots x^{9} + 4.42537 \dots x^{8} + 4.88667 \dots x^{7} + 5.39605 \dots x^{6} + 5.95853 \dots x^{5} + 6.57965 \dots x^{4} + 7.26551 \dots x^{3} + 8.02286 \dots x^{2} + 7.85917 \dots x + 12.67840 \dots \approx 0

Bestimme eine Lösung für

x^{23} + 1.10423 \dots x^{22} + 1.21934 \dots x^{21} + 1.34644 \dots x^{20} + 1.48680 \dots x^{19} + 1.64178 \dots x^{18} + 1.81292 \dots x^{17} + 2.00190 \dots x^{16} + 2.21058 \dots x^{15} + 2.44101 \dots x^{14} + 2.69546 \dots x^{13} + 2.97643 \dots x^{12} + 3.28669 \dots x^{11} + 3.62930 \dots x^{10} + 4.00761 \dots x^{9} + 4.42537 \dots x^{8} + 4.88667 \dots x^{7} + 5.39605 \dots x^{6} + 5.95853 \dots x^{5} + 6.57965 \dots x^{4} + 7.26551 \dots x^{3} + 8.02286 \dots x^{2} + 7.85917 \dots x + 12.67840 \dots = 0

nach dem Newton-Raphson-Verfahren:

x \approx - 1.13250 \dots

Wende die schriftliche Division an:

\frac{x ^{23} + 1.10423 \dots x ^{22} + 1.21934 \dots x ^{21} + 1.34644 \dots x ^{20} + 1.48680 \dots x ^{19} + 1.64178 \dots x ^{18} + 1.81292 \dots x ^{17} + 2.00190 \dots x ^{16} + 2.21058 \dots x ^{15} + 2.44101 \dots x ^{14} + 2.69546 \dots x ^{13} + 2.97643 \dots x ^{12} + 3.28669 \dots x ^{11} + 3.62930 \dots x ^{10} + 4.00761 \dots x ^{9} + 4.42537 \dots x ^{8} + 4.88667 \dots x ^{7} + 5.39605 \dots x ^{6} + 5.95853 \dots x ^{5} + 6.57965 \dots x ^{4} + 7.26551 \dots x ^{3} + 8.02286 \dots x ^{2} + 7.85917 \dots x + 12.67840 \dots}{x + 1.13250 \dots} = x^{22} - 0.02826 \dots x^{21} + 1.25135 \dots x^{20} - 0.07071 \dots x^{19} + 1.56688 \dots x^{18} - 0.13271 \dots x^{17} + 1.96322 \dots x^{16} - 0.22145 \dots x^{15} + 2.46137 \dots x^{14} - 0.34650 \dots x^{13} + 3.08787 \dots x^{12} - 0.52059 \dots x^{11} + 3.87627 \dots x^{10} - 0.76058 \dots x^{9} + 4.86898 \dots x^{8} - 1.08876 \dots x^{7} + 6.11970 \dots x^{6} - 1.53452 \dots x^{5} + 7.69638 \dots x^{4} - 2.13652 \dots x^{3} + 9.68513 \dots x^{2} - 2.94556 \dots x + 11.19503 \dots

x^{22} - 0.02826 \dots x^{21} + 1.25135 \dots x^{20} - 0.07071 \dots x^{19} + 1.56688 \dots x^{18} - 0.13271 \dots x^{17} + 1.96322 \dots x^{16} - 0.22145 \dots x^{15} + 2.46137 \dots x^{14} - 0.34650 \dots x^{13} + 3.08787 \dots x^{12} - 0.52059 \dots x^{11} + 3.87627 \dots x^{10} - 0.76058 \dots x^{9} + 4.86898 \dots x^{8} - 1.08876 \dots x^{7} + 6.11970 \dots x^{6} - 1.53452 \dots x^{5} + 7.69638 \dots x^{4} - 2.13652 \dots x^{3} + 9.68513 \dots x^{2} - 2.94556 \dots x + 11.19503 \dots \approx 0

Bestimme eine Lösung für

x^{22} - 0.02826 \dots x^{21} + 1.25135 \dots x^{20} - 0.07071 \dots x^{19} + 1.56688 \dots x^{18} - 0.13271 \dots x^{17} + 1.96322 \dots x^{16} - 0.22145 \dots x^{15} + 2.46137 \dots x^{14} - 0.34650 \dots x^{13} + 3.08787 \dots x^{12} - 0.52059 \dots x^{11} + 3.87627 \dots x^{10} - 0.76058 \dots x^{9} + 4.86898 \dots x^{8} - 1.08876 \dots x^{7} + 6.11970 \dots x^{6} - 1.53452 \dots x^{5} + 7.69638 \dots x^{4} - 2.13652 \dots x^{3} + 9.68513 \dots x^{2} - 2.94556 \dots x + 11.19503 \dots = 0

nach dem Newton-Raphson-Verfahren:

Keine Lösung für

x \in R

Die Lösungen sind

x \approx 1.10423 \dots, x \approx - 1.13250 \dots

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

so l v e f or x, f = 2 x^{(3)} + 8 f (- 6)

(6 x - 1) (x^{2} + 1) = 0

48 = 3 r^{4}

so l v e f or x, 8 x^{3} + 4 y = 32