Đặt \(a=\sqrt{x^2+1981}\left(a>0\right)\)
\(\Leftrightarrow a^2-x^2=1981\)
Pt tt: \(x^4+a=a^2-x^2\) \(\Leftrightarrow\left(x^4-a^2\right)+\left(a+x^2\right)=0\)
\(\Leftrightarrow\left(x^2-a\right)\left(x^2+a\right)+\left(a+x^2\right)=0\)
\(\Leftrightarrow\left(x^2-a+1\right)\left(a+x^2\right)=0\)
mà \(a+x^2>0\) với \(\forall x;a>0\)
\(\Rightarrow x^2-a+1=0\)
\(\Leftrightarrow x^2+1=\sqrt{x^2+1981}\) \(\Leftrightarrow x^2+x^2-1980=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2=44\\x^2=45\left(vn\right)\end{matrix}\right.\)\(\Rightarrow x=\pm2\sqrt{11}\)
Vậy...
đặt \(x^2=t\left(t\ge0\right)=>t^2+\sqrt{t+1981}=1981\)
\(1981-t^2=\sqrt{t+1981}< =>1981^2-3962t^2+t^4=t+1981\)
\(< =>t^4-3962t^2-t+3922380=0\)
\(< =>\left(t-44\right)\left(t+45\right)\left(t^2-t-1981\right)=0\)
\(=>\left[{}\begin{matrix}t=44\left(TM\right)\\t=-45\left(loai\right)\end{matrix}\right.\)
\(=>t=44=>x=\pm2\sqrt{11}\)
vậy...
