2sqrt(x^2-a^2)=4x-2a

Lösung

2 x^{2} - a^{2} = 4 x - 2 a

Keine L \overset{o}{¨} sung f \overset{u}{¨} r x \in R

Schritte zur Lösung

2 x^{2} - a^{2} = 4 x - 2 a

Quadriere beide Seiten:

4 x^{2} - 4 a^{2} = 16 x^{2} - 16 a x + 4 a^{2}

4 x^{2} - 4 a^{2} = 16 x^{2} - 16 a x + 4 a^{2}

Löse

4 x^{2} - 4 a^{2} = 16 x^{2} - 16 a x + 4 a^{2} : x = \frac{2 a}{3} + i \frac{2 a}{3}, x = \frac{2 a}{3} - i \frac{2 a}{3}

x = \frac{2 a}{3} + i \frac{2 a}{3}, x = \frac{2 a}{3} - i \frac{2 a}{3}

Entferne komplexe Lösungen

: x = \frac{2 a}{3} + i \frac{2 a}{3}, x = \frac{2 a}{3} - i \frac{2 a}{3}

Keine L \overset{o}{¨} sung f \overset{u}{¨} r x \in R

x - 1 - 9 = 2

so l v e f or x, x + x - 1 = 3

2 x^{3} + 2 x^{2} + 4 x + 1 = 3

(x + 2 - x) = 2

so l v e f or x, - 5 + x + 6 = 3