\(\sqrt{x^4+3x^2}+\sqrt{x^4+6x^2}\)
\(=\sqrt{x^4+\dfrac{3}{2}x^2+\dfrac{3}{2}x^2+\dfrac{9}{4}-\dfrac{9}{4}}+\sqrt{x^4+3x^2+3x^2+9-9}\)
\(=\sqrt{\left(x^2+\dfrac{3}{2}\right)^2-\left(\dfrac{3}{2}\right)^2}+\sqrt{\left(x^2+3\right)^2-3^2}\)
\(=\sqrt{\left(x^2+\dfrac{3}{2}-\dfrac{3}{2}\right)\left(x^2+\dfrac{3}{2}+\dfrac{3}{2}\right)}+\sqrt{\left(x^2+3-3\right)\left(x^2+3+3\right)}\)
\(=\sqrt{x^2}.\sqrt{x^2+3}+\sqrt{x^2}.\sqrt{x^2+6}\)
\(=x\left(\sqrt{x^2+3}+\sqrt{x^2+6}\right)\)
\(\sqrt{x^4+3x^2}+\sqrt{x^4+6x^2}\)
\(=\sqrt{x^4+3x^2+\dfrac{9}{4}-\dfrac{9}{4}}+\sqrt{x^4+6x^2+9-9}\)
\(=\sqrt{\left(x^2+\dfrac{3}{2}\right)^2-\dfrac{9}{4}}+\sqrt{\left(x^2+3\right)^2-9}\)
\(=\left|x^2+\dfrac{3}{2}\right|-\dfrac{3}{2}+\left|x^2+3\right|-3\)
Vì: \(\left\{{}\begin{matrix}x^2+\dfrac{3}{2}>0\\x^2+3>0\end{matrix}\right.\)
Nên: \(pt\Leftrightarrow x^2+\dfrac{3}{2}-\dfrac{3}{2}+x^2+3-3\)
\(=2x^2\)
Đừng giết em :333333333
