solvefor x,cuadratica=x^2+4

解

解く

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

解答ステップ

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

代用

x = u + v i

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

拡張

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

標準的な複素数形式で

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

を書き換える:

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

複素数は, その実数部と虚数部が等しい場合にのみ等しくなるequation系として書き換える:

[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}

代用を戻す

x = u + v 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 - \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