\(ĐKXĐ:\)a,b,c đôi một khác nhau.
\(\dfrac{x}{\left(a-b\right).\left(a-c\right)}+\dfrac{x}{\left(b-a\right).\left(b-c\right)}+\dfrac{x}{\left(c-a\right).\left(c-b\right)}=2\)
\(\Leftrightarrow x\left(\dfrac{1}{\left(a-b\right).\left(a-c\right)}+\dfrac{1}{\left(b-a\right).\left(b-c\right)}+\dfrac{1}{\left(c-a\right).\left(c-b\right)}\right)=2\)
\(\Leftrightarrow x\left(\dfrac{-\left(b-c\right)-\left(c-a\right)-\left(a-b\right)}{\left(a-b\right).\left(b-c\right).\left(c-a\right)}\right)=2\)
\(\Leftrightarrow x\left(\dfrac{-b+c-c+a-a+b}{\left(a-b\right).\left(b-c\right).\left(c-a\right)}\right)=2\)
\(\Leftrightarrow x\left(\dfrac{0}{\left(a-b\right).\left(b-c\right).\left(c-a\right)}\right)=2\)
\(\Rightarrow0x=2\) (vô lý)
-Vậy khi a,b,c đôi một khác nhau thì phương trình vô nghiệm.
