solvefor x,x^{2/3}+y^{2/3}=a^{2/3}

Lösung

löse nach

x, x^{\frac{2}{3}} + y^{\frac{2}{3}} = a^{\frac{2}{3}}

x = a^{2} - 3 a^{\frac{4}{3}} y^{\frac{2}{3}} + 3 a^{\frac{2}{3}} y^{\frac{4}{3}} - y^{2}, x = - a^{2} - 3 a^{\frac{4}{3}} y^{\frac{2}{3}} + 3 a^{\frac{2}{3}} y^{\frac{4}{3}} - y^{2}

Schritte zur Lösung

x^{\frac{2}{3}} + y^{\frac{2}{3}} = a^{\frac{2}{3}}

Verschiebe

y^{\frac{2}{3}}

auf die rechte Seite

x^{\frac{2}{3}} = a^{\frac{2}{3}} - y^{\frac{2}{3}}

Potenziere beide Seiten der Gleichung mit

3 : x^{2} = a^{2} - 3 a^{\frac{4}{3}} y^{\frac{2}{3}} + 3 a^{\frac{2}{3}} y^{\frac{4}{3}} - y^{2}

x^{2} = a^{2} - 3 a^{\frac{4}{3}} y^{\frac{2}{3}} + 3 a^{\frac{2}{3}} y^{\frac{4}{3}} - y^{2}

Löse

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

x = a^{2} - 3 a^{\frac{4}{3}} y^{\frac{2}{3}} + 3 a^{\frac{2}{3}} y^{\frac{4}{3}} - y^{2}, x = - a^{2} - 3 a^{\frac{4}{3}} y^{\frac{2}{3}} + 3 a^{\frac{2}{3}} y^{\frac{4}{3}} - y^{2}

x + 2 = 2 x + 1

x - 1 - 2 x + 1 = 0

(x - 2)^{\frac{2}{3}} + (x - 2)^{\frac{1}{3}} - 2 = 0

3 x - 27 = 0

x^{\frac{3}{2}} + (x^{2})^{- 2} + x^{3} = 4