x^3-333^3=444^3+555^3

Lösung

x^{3} - 33 3^{3} = 44 4^{3} + 55 5^{3}

x = 3295408296, x = - 3295408296 \frac{1}{2} + 3295408296 \frac{3}{2} i, x = - 3295408296 \frac{1}{2} - 3295408296 \frac{3}{2} i

Schritte zur Lösung

x^{3} - 33 3^{3} = 44 4^{3} + 55 5^{3}

Verschiebe

33 3^{3}

auf die rechte Seite

x^{3} = 295408296

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 = 3295408296, x = 3295408296 \frac{- 1 + 3 i}{2}, x = 3295408296 \frac{- 1 - 3 i}{2}

Vereinfache

3295408296 \frac{- 1 + 3 i}{2} : - 3295408296 \frac{1}{2} + 3295408296 \frac{3}{2} i

Vereinfache

3295408296 \frac{- 1 - 3 i}{2} : - 3295408296 \frac{1}{2} - 3295408296 \frac{3}{2} i

x = 3295408296, x = - 3295408296 \frac{1}{2} + 3295408296 \frac{3}{2} i, x = - 3295408296 \frac{1}{2} - 3295408296 \frac{3}{2} i

x^{2} (x^{2} - 3) = 4

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

z^{4} + 32 z^{2} - 144 = 0

3 x^{3} + x^{2} - 13 x + 5 = 0

- x^{3} + 2 x = 0