Đặt \(x^2+1=a\)
\(\Rightarrow\frac{a}{120}+\frac{a+1}{119}+\frac{a+2}{118}=3\)
\(\Leftrightarrow21241a=2506200\)
\(\Leftrightarrow a=\frac{2506200}{21241}\)
\(\Rightarrow x=.....\)
\(\frac{x^2}{120}+\frac{x^2+1}{119}+\frac{x^2+2}{118}=3\)
\(\Leftrightarrow\frac{x^2}{120}+1+\frac{x^2+1}{119}+1+\frac{x^2+2}{118}+1=6\)
\(\Leftrightarrow\frac{x^2+120}{120}+\frac{x^2+120}{119}+\frac{x^2+120}{118}=6\)
\(\Leftrightarrow\left(x^2+120\right)\left(\frac{1}{120}+\frac{1}{119}+\frac{1}{118}\right)=6\)
\(\Leftrightarrow x^2+120=\frac{6}{\frac{1}{120}+\frac{1}{119}+\frac{1}{118}}\)
\(\Leftrightarrow x^2=\frac{6}{\frac{1}{120}+\frac{1}{119}+\frac{1}{118}}-1\)
\(\Leftrightarrow\orbr{\begin{cases}x=\sqrt{\frac{6}{\frac{1}{120}+\frac{1}{119}+\frac{1}{118}}-1}\\x=-\sqrt{\frac{6}{\frac{1}{120}+\frac{1}{119}+\frac{1}{118}-1}}\end{cases}}\)
