原方程即:
2x*[a/(ab+a+1)+b/(bc+b+1)+c/(ca+c+1)]=4
x*[a/(ab+a+1)+b/(bc+b+1)+c/(ca+c+1)]=2····①
关键是先求出中括号的值:
a/(ab+a+1)+b/(bc+b+1)+c/(ca+c+1)·····注:不断将abc=1替换分母中的1;
=a/(ab+a+abc)+b/(bc+b+1)+c/(ca+c+1)
=1/(b+1+bc)+b/(bc+b+1)+c/(ca+c+1)
=(1+b)/(bc+b+1)+c/(ca+c+1)
=(abc+b)/(bc+b+abc)+c/(ca+c+1)
=(ac+1)/(c+1+ac)+c/(ca+c+1)
=(ac+c+1)/(ac+c+1)
=1
所以,方程①就变成:
x=2
即为所求.
关于上面部分过程,可以参考我以前的回答: