解
ax2−bx+9+3i=0
解
x=2a−8a2b2+b4+1440a2−72ab2−36ab−8a2b2+1440a2−72ab2+b4−36a−3+−8a2−36a+b2+1440a2−72ab2+b4i,x=−2a−8a2b2+b4+1440a2−72ab2−36a−b−8a2b2+1440a2−72ab2+b4−36a−3−−8a2−36a+b2+1440a2−72ab2+b4i,x=2a−8a2b2−b4+1440a2−72ab2−36ab−8a2b2−36a−1440a2−72ab2+b4−3+−8a2−36a+b2−1440a2−72ab2+b4i,x=−2a−8a2b2−b4+1440a2−72ab2−36a−b−8a2b2−36a−1440a2−72ab2+b4−3−−8a2−36a+b2−1440a2−72ab2+b4i
解答ステップ
ax2−bx+9+3i=0
代用 x=u+via(u+vi)2−b(u+vi)+9+3i=0
拡張 a(u+vi)2−b(u+vi)+9+3i:(au2−av2−bu+9)+i(3−bv+2auv)
(au2−av2−bu+9)+i(3−bv+2auv)=0
標準的な複素数形式で 0 を書き換える:0+0i(au2−av2−bu+9)+i(3−bv+2auv)=0+0i
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:[au2−av2−bu+9=03−bv+2auv=0]
[au2−av2−bu+9=03−bv+2auv=0]:u=2a−8a2b2+b4+1440a2−72ab2−36ab−8a2b2+1440a2−72ab2+b4−36a−3,u=−2a−8a2b2+b4+1440a2−72ab2−36a−b−8a2b2+1440a2−72ab2+b4−36a−3,u=2a−8a2b2−b4+1440a2−72ab2−36ab−8a2b2−36a−1440a2−72ab2+b4−3,u=−2a−8a2b2−b4+1440a2−72ab2−36a−b−8a2b2−36a−1440a2−72ab2+b4−3,v=−8a2−36a+b2+1440a2−72ab2+b4v=−−8a2−36a+b2+1440a2−72ab2+b4v=−8a2−36a+b2−1440a2−72ab2+b4v=−−8a2−36a+b2−1440a2−72ab2+b4
代用を戻す x=u+vix=2a−8a2b2+b4+1440a2−72ab2−36ab−8a2b2+1440a2−72ab2+b4−36a−3+−8a2−36a+b2+1440a2−72ab2+b4i,x=−2a−8a2b2+b4+1440a2−72ab2−36a−b−8a2b2+1440a2−72ab2+b4−36a−3−−8a2−36a+b2+1440a2−72ab2+b4i,x=2a−8a2b2−b4+1440a2−72ab2−36ab−8a2b2−36a−1440a2−72ab2+b4−3+−8a2−36a+b2−1440a2−72ab2+b4i,x=−2a−8a2b2−b4+1440a2−72ab2−36a−b−8a2b2−36a−1440a2−72ab2+b4−3−−8a2−36a+b2−1440a2−72ab2+b4i