解答
ax2−bx+9+3i=0
解答
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
求解步骤
ax2−bx+9+3i=0
替代 x=u+via(u+vi)2−b(u+vi)+9+3i=0
展开 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
将 0 改写成标准复数形式:0+0i(au2−av2−bu+9)+i(3−bv+2auv)=0+0i
复数仅在实部和虚部均相等时才相等改写为方程组:[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
x=u+vi代回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