解答
25x2+60x+37=0a+bia+bi
解答
x=50−50−1+b2+1+a2b2+2ab2b+ab−60−50−1+b2+a2b2+2ab2+1+−50−1+b2+a2b2+2ab2+1i,x=−50−50−1+b2+1+a2b2+2ab2b+ab+60−50−1+b2+a2b2+2ab2+1−−50−1+b2+a2b2+2ab2+1i,x=521+b2+1+a2b2+2ab2b+ab−62b2+a2b2+2ab2+1+1+52b2+a2b2+2ab2+1+1i,x=−521+b2+1+a2b2+2ab2b+ab+62b2+a2b2+2ab2+1+1−52b2+a2b2+2ab2+1+1i
求解步骤
25x2+60x+37=0⋅a+bia+bi
替代 x=u+vi25(u+vi)2+60(u+vi)+37=0⋅a+bia+bi
乘开
(25u2−25v2+60u+37)+i(60v+50uv)=i(b+ab)
将 i(b+ab) 改写成标准复数形式:0+(b+ab)i(25u2−25v2+60u+37)+i(60v+50uv)=0+(b+ab)i
复数仅在实部和虚部均相等时才相等改写为方程组:[25u2−25v2+60u+37=060v+50uv=b+ab]
[25u2−25v2+60u+37=060v+50uv=b+ab]:u=50−50−1+b2+1+a2b2+2ab2b+ab−60−50−1+b2+a2b2+2ab2+1,u=−50−50−1+b2+1+a2b2+2ab2b+ab+60−50−1+b2+a2b2+2ab2+1,u=521+b2+1+a2b2+2ab2b+ab−62b2+a2b2+2ab2+1+1,u=−521+b2+1+a2b2+2ab2b+ab+62b2+a2b2+2ab2+1+1,v=−50−1+b2+a2b2+2ab2+1v=−−50−1+b2+a2b2+2ab2+1v=52b2+a2b2+2ab2+1+1v=−52b2+a2b2+2ab2+1+1
x=u+vi代回x=50−50−1+b2+1+a2b2+2ab2b+ab−60−50−1+b2+a2b2+2ab2+1+−50−1+b2+a2b2+2ab2+1i,x=−50−50−1+b2+1+a2b2+2ab2b+ab+60−50−1+b2+a2b2+2ab2+1−−50−1+b2+a2b2+2ab2+1i,x=521+b2+1+a2b2+2ab2b+ab−62b2+a2b2+2ab2+1+1+52b2+a2b2+2ab2+1+1i,x=−521+b2+1+a2b2+2ab2b+ab+62b2+a2b2+2ab2+1+1−52b2+a2b2+2ab2+1+1i