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Beliebt Algebra >

x^2-6x+9=4sqrt(x^2-6x+6)

Lösung

x^{2} - 6 x + 9 = 4 x^{2} - 6 x + 6

Lösung

x = 1, x = 5, x = 3 + 23, x = 3 - 23

+1

Dezimale

x = 1, x = 5, x = 6.46410 \dots, x = - 0.46410 \dots

Schritte zur Lösung

x^{2} - 6 x + 9 = 4 x^{2} - 6 x + 6

Quadriere beide Seiten:

x^{4} - 12 x^{3} + 54 x^{2} - 108 x + 81 = 16 x^{2} - 96 x + 96

x^{4} - 12 x^{3} + 54 x^{2} - 108 x + 81 = 16 x^{2} - 96 x + 96

Löse

x^{4} - 12 x^{3} + 54 x^{2} - 108 x + 81 = 16 x^{2} - 96 x + 96 : x = 1, x = 5, x = 3 + 23, x = 3 - 23

x = 1, x = 5, x = 3 + 23, x = 3 - 23

Überprüfe die Lösungen:

x = 1

Wahr

, x = 5

Wahr

, x = 3 + 23

Wahr

, x = 3 - 23

Wahr

Die Lösungen sind

x = 1, x = 5, x = 3 + 23, x = 3 - 23

Graph

Beliebte Beispiele

8 = x^{\frac{3}{2}}

5 x + 4 + 2 = x

6(x+6)^{2/3}=54

6 (x + 6)^{\frac{2}{3}} = 54

2 x - 6 = 10

3 x - 6 = 6