Question

若abc=1,解关于x的方程：2ax 2bx 2cx

Answer 1

a/(ab+a+1)=ac/(ab+a+abc)c=ac/(ac+c+1)

2ax/(ab+a+1)+2bx/(bc+b+1)+2cx/(ac+c+1)=1

xac/(ac+c+1)+cx/(ac+c+1)+bx/(bc+b+1)=1/2

[(ac+c+1)-1]x/(ac+c+1)+bx/(bc+b+1)=1/2

x(1-1/(ac+c+1)+b/(bc+b+1)]=1/2

x(1-1/(ac+c+1)+b/(bc+b+abc))=1/2

x(1-1/(ac+c+1)+1/(ac+c+1))=1/2

x=1/2