4r^3s+864s^4=4s(r+6s)

Lösung

4 r^{3} s + 864 s^{4} = 4 s (r + 6 s)

s = 0, s = - \frac{r}{6}, s = \frac{r + - 3 r ^{2} + 4}{12}, s = \frac{r - - 3 r ^{2} + 4}{12}

Schritte zur Lösung

4 r^{3} s + 864 s^{4} = 4 s (r + 6 s)

Verschiebe

4 s (r + 6 s)

auf die linke Seite

4 r^{3} s + 864 s^{4} - 4 s (r + 6 s) = 0

Faktorisiere

4 r^{3} s + 864 s^{4} - 4 s (r + 6 s) : 4 s (r + 6 s) (r^{2} + 36 s^{2} - 6 rs - 1)

4 s (r + 6 s) (r^{2} + 36 s^{2} - 6 rs - 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

s = 0 or r + 6 s = 0 or r^{2} + 36 s^{2} - 6 rs - 1 = 0

Löse

r + 6 s = 0 : s = - \frac{r}{6}

Löse

r^{2} + 36 s^{2} - 6 rs - 1 = 0 : s = \frac{r + - 3 r ^{2} + 4}{12}, s = \frac{r - - 3 r ^{2} + 4}{12}

Die Lösungen sind

s = 0, s = - \frac{r}{6}, s = \frac{r + - 3 r ^{2} + 4}{12}, s = \frac{r - - 3 r ^{2} + 4}{12}

(x - 14)^{2} + 13 = 12

ab x^{2} = (a - b)^{2} (x + 1)

- 6 x^{2} - 586 = 84 x - 484 x - 4

so l v e f or x, x^{2} + 7 x + 12 = 0

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