solvefor y,6-x^2-y^2=sqrt(x^2+y^2)

Lösung

löse nach

y, 6 - x^{2} - y^{2} = x^{2} + y^{2}

y = - x^{2} + 4 {- 2 \leq x \leq 2}, y = - - x^{2} + 4 {- 2 \leq x \leq 2}

Schritte zur Lösung

6 - x^{2} - y^{2} = x^{2} + y^{2}

Quadriere beide Seiten:

2 y^{2} x^{2} - 12 x^{2} + x^{4} - 12 y^{2} + y^{4} + 36 = x^{2} + y^{2}

2 y^{2} x^{2} - 12 x^{2} + x^{4} - 12 y^{2} + y^{4} + 36 = x^{2} + y^{2}

Löse

2 y^{2} x^{2} - 12 x^{2} + x^{4} - 12 y^{2} + y^{4} + 36 = x^{2} + y^{2} : y = - x^{2} + 9, y = - - x^{2} + 9, y = - x^{2} + 4, y = - - x^{2} + 4

y = - x^{2} + 9, y = - - x^{2} + 9, y = - x^{2} + 4, y = - - x^{2} + 4

Überprüfe die Lösungen:

y = - x^{2} + 9

Falsch

, y = - - x^{2} + 9

Falsch

, y = - x^{2} + 4 {- 2 \leq x \leq 2}, y = - - x^{2} + 4 {- 2 \leq x \leq 2}

Die Lösungen sind

y = - x^{2} + 4 {- 2 \leq x \leq 2}, y = - - x^{2} + 4 {- 2 \leq x \leq 2}

8 x + 24 - 6 = - 2

x + 8 + 2 = 5

x = 6 x - 15

\frac{1}{2} x^{2} = 2 x + 1

\frac{- 2 x ^{2} + 100}{100 - x ^{2}} = 0