X^3=303^3+404^3+505^3

Lösung

X^{3} = 30 3^{3} + 40 4^{3} + 50 5^{3}

X = 3222545016, X = - 3222545016 \frac{1}{2} + 3222545016 \frac{3}{2} i, X = - 3222545016 \frac{1}{2} - 3222545016 \frac{3}{2} i

Schritte zur Lösung

X^{3} = 30 3^{3} + 40 4^{3} + 50 5^{3}

Vereinfache

30 3^{3} + 40 4^{3} + 50 5^{3} : 222545016

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 = 3222545016, X = 3222545016 \frac{- 1 + 3 i}{2}, X = 3222545016 \frac{- 1 - 3 i}{2}

Vereinfache

3222545016 \frac{- 1 + 3 i}{2} : - 3222545016 \frac{1}{2} + 3222545016 \frac{3}{2} i

Vereinfache

3222545016 \frac{- 1 - 3 i}{2} : - 3222545016 \frac{1}{2} - 3222545016 \frac{3}{2} i

X = 3222545016, X = - 3222545016 \frac{1}{2} + 3222545016 \frac{3}{2} i, X = - 3222545016 \frac{1}{2} - 3222545016 \frac{3}{2} i

(u^{2} - 6 u + 8) (2 u + 14) = 0

X^{4} - X^{2} + 1 = 0

4 x^{3} = 16 x

1 - 9 x - 6 x - x^{3} = 0

6 - 3 (x + 1) = - 4 x^{2} (1 - x)