solvefor x,cuadratica=x^2+4

Lösung

löse nach

x, c u a d r a t i c a = x^{2} + 4

x = \frac{c ^{2} a ^{3} d u r t}{2 - \frac{- 4 + c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16}{2}} + - \frac{- 4 + c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16}{2} i, x = - \frac{c ^{2} a ^{3} d u r t}{2 - \frac{- 4 + c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16}{2}} - - \frac{- 4 + c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16}{2} i, x = \frac{c ^{2} a ^{3} d u r t}{2 c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16 + 4} + \frac{c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16 + 4}{2} i, x = - \frac{c ^{2} a ^{3} d u r t}{2 c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16 + 4} - \frac{c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16 + 4}{2} i

Schritte zur Lösung

c u a d r a t i c a = x^{2} + 4

Ersetze

x = u + v i

c u a d r a t i c a = (u + v i)^{2} + 4

Schreibe um

i c^{2} a^{3} d u r t = (u^{2} - v^{2} + 4) + 2 i uv

Schreibe

i c^{2} a^{3} d u r t

in der Standard komplexen Form um:

0 + c^{2} a^{3} d u r t i

0 + c^{2} a^{3} d u r t i = (u^{2} - v^{2} + 4) + 2 i uv

Komplexe Zahlen können nur gleich sein wenn ihre realen und imaginären Teile gleich sind.Schreibe als Gleichungssystem um

[0 = u^{2} - v^{2} + 4 c^{2} a^{3} d u r t = 2 uv]

[0 = u^{2} - v^{2} + 4 c^{2} a^{3} d u r t = 2 uv] : u = \frac{c ^{2} a ^{3} d u r t}{2 - \frac{- 4 + c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16}{2}}, u = - \frac{c ^{2} a ^{3} d u r t}{2 - \frac{- 4 + c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16}{2}}, u = \frac{c ^{2} a ^{3} d u r t}{2 c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16 + 4}, u = - \frac{c ^{2} a ^{3} d u r t}{2 c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16 + 4}, v = - \frac{- 4 + c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16}{2} v = - - \frac{- 4 + c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16}{2} v = \frac{c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16 + 4}{2} v = - \frac{c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16 + 4}{2}

Setze in

x = u + v i

ein

x = \frac{c ^{2} a ^{3} d u r t}{2 - \frac{- 4 + c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16}{2}} + - \frac{- 4 + c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16}{2} i, x = - \frac{c ^{2} a ^{3} d u r t}{2 - \frac{- 4 + c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16}{2}} - - \frac{- 4 + c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16}{2} i, x = \frac{c ^{2} a ^{3} d u r t}{2 c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16 + 4} + \frac{c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16 + 4}{2} i, x = - \frac{c ^{2} a ^{3} d u r t}{2 c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16 + 4} - \frac{c ^{4} a ^{6} d ^{2} u ^{2} r ^{2} t ^{2} + 16 + 4}{2} i

so l v e f or r, i = \frac{e}{r}

x + y i = 3 - 2 i

Z^{2} = 3 - 4 i

6 i = (x + i) (y + i) + 1

i y (2 - i) + 1 = 4 i - x (1 - i)