Question

\(5x^4-2x^2-3x^2\sqrt{x^2+2}=4\)

Answer 1

Nhận thấy \(x=0\) không phải nghiệm, chia 2 vế cho \(x^4\) ta được:

\(5-\frac{2}{x^2}-3\sqrt{\frac{1}{x^2}+\frac{2}{x^4}}=\frac{4}{x^4}\)

\(\Leftrightarrow2\left(\frac{2}{x^4}+\frac{1}{x^2}\right)+3\sqrt{\frac{2}{x^4}+\frac{1}{x^2}}-5=0\)

Đặt \(\sqrt{\frac{2}{x^4}+\frac{1}{x^2}}=a>0\) ta được:

\(2a^2+3a-5=0\Rightarrow\left[{}\begin{matrix}a=1\\a=-\frac{5}{2}< 0\left(l\right)\end{matrix}\right.\)

\(\Rightarrow\sqrt{\frac{2}{x^4}+\frac{1}{x^2}}=1\Leftrightarrow\frac{2}{x^4}+\frac{1}{x^2}-1=0\)

\(\Leftrightarrow-x^4+x^2+2=0\Rightarrow\left[{}\begin{matrix}x^2=-1\left(l\right)\\x^2=2\end{matrix}\right.\) \(\Rightarrow x=\pm\sqrt{2}\)