\(\sqrt{x^2+12}+5=3x+\sqrt{x^2+5}\\ \Leftrightarrow\sqrt{x^2+12}-\sqrt{x^2+5}=3x-5\\ \Leftrightarrow\left(\sqrt{x^2+12}-\sqrt{x^2+5}\right)=\left(3x-5\right)^2\\ \Leftrightarrow2x^2+17-2\sqrt{\left(x^2+12\right)\left(x^2+5\right)}=9x^2-30x+25\\ 7x^2-30x+8=-2\sqrt{\left(x^2+12\right)\left(x^2+5\right)}\\ \Leftrightarrow\left(7x^2-30x+8\right)^2=\left(-2\sqrt{\left(x^2+12\right)\left(x^2+5\right)}\right)^2\\ \Leftrightarrow49x^4-420x^3+1012x^2-480x+64=4x^4+68x^2+240\\ \Leftrightarrow45x^4-420x^3+944x^2-480x-176=0\Leftrightarrow\left(x-2\right)\left(45x^3-330x^2+284x+88\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-2=0\\45x^3-330x^2+284x+88=0\end{matrix}\right.\Rightarrow x=2\)
cái phương trình thứ 2 mình ko bt giải, thông cảm nha :))