Question

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

Answer 1

\(x=0\) không phải nghiệm, chia 2 vế cho \(x^4\)

\(\Leftrightarrow5-\frac{2}{x^2}-3\sqrt{\frac{1}{x^2}+\frac{2}{x^4}}=\frac{4}{x^4}\)

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

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

\(\Rightarrow2a^2+3a-5=0\Rightarrow\left[{}\begin{matrix}a=1\\a=-\frac{5}{2}\left(l\right)\end{matrix}\right.\)

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