\(x^4+\sqrt{x^2+2017}=2017\)
\(\Leftrightarrow x^4+x^2+\frac{1}{4}=x^2+2017-\sqrt{x^2+2017}+\frac{1}{4}\)
\(\Leftrightarrow\left(x^2+\frac{1}{2}\right)^2=\left(\sqrt{x^2+2017}-\frac{1}{2}\right)^2\)
\(\Leftrightarrow x^2+\frac{1}{2}=\sqrt{x^2+2017}-\frac{1}{2}\)(vì \(\sqrt{x^2+2017}>\frac{1}{2}\))
\(\Leftrightarrow x^2-\sqrt{x^2+2017}+1=0\)
\(\Leftrightarrow\left(x^2+2017-\sqrt{x^2+2017}+\frac{1}{4}\right)=\frac{8065}{4}\)
\(\Leftrightarrow\left(\sqrt{x^2+2017}-\frac{1}{2}\right)^2=\frac{8065}{4}\)
\(\Leftrightarrow\sqrt{x^2+2017}=\frac{\sqrt{8065}+1}{2}\)
\(\Leftrightarrow x^2=\frac{\left(\sqrt{8065}+1\right)^2}{4}-2017\)
\(\Leftrightarrow\orbr{\begin{cases}x=\sqrt{\frac{\left(\sqrt{8065}+1\right)^2}{4}-2017}\\x=-\sqrt{\frac{\left(\sqrt{8065}+1\right)^2}{4}-2017}\end{cases}}\)
