解方程mnx²;-(m²;+n²;)x+mn=0(mn≠0)

解方程mnx²;-(m²;+n²;)x+mn=0(mn≠0)


mnx²;-(m²;+ n²;)x + mn = 0
(mx -n)(nx -m)= 0
x = n/m或x = m/n



m/mx-n—2/x = -n/nx+m(m^2-n^2≠0,mn≠0)解這個方程


m/(mX-n)+n/(nX+m)=2/X
[m(nX+m)+n(mX-n)] / [(mX-n)(nX+m)]=2/X
(m^2-n^2+2mnX)/ [(mn)X^2+(m^2-n^2)X-mn]=2/X
(m^2-n^2+2mnX)X=2[(mn)X^2+(m^2-n^2)X-mn]
(m^2-n^2)X-2mn=0
X=2mn/(m^2-n^2)



解方程x²;+mx-nx-mn=0(m.n為非零數)


x^2+(m-n)x-mn=0
(x+m)(x-n)=0
x=-m,n