x/(x2+2)+(x2+20/x=-10/3,求X的值

题目

x/(x2+2)+(x2+20/x=-10/3,求X的值

答案

令a=x/(x²+2)
则(x²+2)/x=1/a
a+1/a=-10/3
3a²+10a+3=0
(3a+1)(a+3)=0
a=-1/3,a=-3
x/(x²+2)=-1/3
x²+2=-3x
x²+3x+2=0
(x+1)(x+2)=0
x=-1,x=-2
x/(x²+2)=-3
3x²+6=-x
3x²+x+6=0
无解
所以x=-1,x=-2