solvefor x,y^2=kx^3

Lösung

löse nach

x, y^{2} = k x^{3}

x = 3 \frac{y ^{2}}{k}, x = - \frac{3 \frac{y ^{2}}{k}}{2} + \frac{3 \frac{y ^{2}}{k} 3}{2} i, x = - \frac{3 \frac{y ^{2}}{k}}{2} - \frac{3 \frac{y ^{2}}{k} 3}{2} i; k \neq = 0

Schritte zur Lösung

y^{2} = k x^{3}

Tausche die Seiten

k x^{3} = y^{2}

Teile beide Seiten durch

k; k \neq = 0

x^{3} = \frac{y ^{2}}{k}; k \neq = 0

Für

x^{3} = f (a)

sind die Lösungen

x = 3 f (a), 3 f (a) \frac{- 1 - 3 i}{2}, 3 f (a) \frac{- 1 + 3 i}{2}

x = 3 \frac{y ^{2}}{k}, x = 3 \frac{y ^{2}}{k} \frac{- 1 + 3 i}{2}, x = 3 \frac{y ^{2}}{k} \frac{- 1 - 3 i}{2}; k \neq = 0

Vereinfache

3 \frac{y ^{2}}{k} \frac{- 1 + 3 i}{2} : - \frac{3 \frac{y ^{2}}{k}}{2} + \frac{3 \frac{y ^{2}}{k} 3}{2} i

Vereinfache

3 \frac{y ^{2}}{k} \frac{- 1 - 3 i}{2} : - \frac{3 \frac{y ^{2}}{k}}{2} - \frac{3 \frac{y ^{2}}{k} 3}{2} i

x = 3 \frac{y ^{2}}{k}, x = - \frac{3 \frac{y ^{2}}{k}}{2} + \frac{3 \frac{y ^{2}}{k} 3}{2} i, x = - \frac{3 \frac{y ^{2}}{k}}{2} - \frac{3 \frac{y ^{2}}{k} 3}{2} i; k \neq = 0

roo t s x^{6} - 64

x^{3} + 7 x^{2} + 4 x - 12 = 0

x^{5} - 5 x^{3} = 36 x

x^{4} - 8 x^{3} + 16 x^{2} = 0

x^{3} - 17 x - 4 = 0