(b)sqrt(x^2-1)=x-3

Lösung

(b) x^{2} - 1 = x - 3

x = \frac{3 + b b ^{2} + 8}{1 - b ^{2}}, x = \frac{3 - b b ^{2} + 8}{1 - b ^{2}}

Schritte zur Lösung

(b) x^{2} - 1 = x - 3

Quadriere beide Seiten:

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

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

Löse

b^{2} x^{2} - b^{2} = x^{2} - 6 x + 9 : x = \frac{3 + b b ^{2} + 8}{1 - b ^{2}}, x = \frac{3 - b b ^{2} + 8}{1 - b ^{2}}

x = \frac{3 + b b ^{2} + 8}{1 - b ^{2}}, x = \frac{3 - b b ^{2} + 8}{1 - b ^{2}}

Überprüfe die Lösungen:

x = \frac{3 + b b ^{2} + 8}{1 - b ^{2}}

Wahr

, x = \frac{3 - b b ^{2} + 8}{1 - b ^{2}}

Wahr

Die Lösungen sind

x = \frac{3 + b b ^{2} + 8}{1 - b ^{2}}, x = \frac{3 - b b ^{2} + 8}{1 - b ^{2}}

x^{2} + 4 x = (x^{2}) + 4 x

x - 4 - 9 x = 0

12 x + 2 x - 2 = 0

x + 3 = 3

x^{2} - 5 = x + 2