![\sqrt{x^2+32}-2\sqrt[4]{x^2+32}=3](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2%2B32%7D-2%5Csqrt%5B4%5D%7Bx%5E2%2B32%7D%3D3 "\sqrt{x^2+32}-2\sqrt[4]{x^2+32}=3")
1) ОДЗ:
0\Rightarrow D(y)=\mathbb{R}" alt="\left(\forall x\in\mathbb{R}\right)x^2+32>0\Rightarrow D(y)=\mathbb{R}" align="absmiddle" class="latex-formula">
2) Пусть ![\sqrt[4]{x^2+32}=\varphi](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%5E2%2B32%7D%3D%5Cvarphi "\sqrt[4]{x^2+32}=\varphi")
, тогда 
.
0\medskip\\\varphi^2-2\varphi-3=0\end{cases}\!\!\!\!\!\!\Leftrightarrow\begin{cases}\varphi>0\medskip\\\left[\begin{gathered}\varphi=-1\\\varphi=3\end{gathered}\end{cases}\!\!\!\!\!\!\Leftrightarrow\varphi=3" alt="\begin{cases}\varphi>0\medskip\\\varphi^2-2\varphi-3=0\end{cases}\!\!\!\!\!\!\Leftrightarrow\begin{cases}\varphi>0\medskip\\\left[\begin{gathered}\varphi=-1\\\varphi=3\end{gathered}\end{cases}\!\!\!\!\!\!\Leftrightarrow\varphi=3" align="absmiddle" class="latex-formula">
3) Возвращаемся к иксу
![\begin{cases}\sqrt[4]{x^2+32}=\varphi\smallskip\\\varphi=3\end{cases}\!\!\!\!\!\!\Leftrightarrow\sqrt[4]{x^2+32}=3\Leftrightarrow x^2+32=81\Leftrightarrow x^2=49\Leftrightarrow x\in\left\{-7;7\right\}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%5Csqrt%5B4%5D%7Bx%5E2%2B32%7D%3D%5Cvarphi%5Csmallskip%5C%5C%5Cvarphi%3D3%5Cend%7Bcases%7D%5C%21%5C%21%5C%21%5C%21%5C%21%5C%21%5CLeftrightarrow%5Csqrt%5B4%5D%7Bx%5E2%2B32%7D%3D3%5CLeftrightarrow%20x%5E2%2B32%3D81%5CLeftrightarrow%20x%5E2%3D49%5CLeftrightarrow%20x%5Cin%5Cleft%5C%7B-7%3B7%5Cright%5C%7D "\begin{cases}\sqrt[4]{x^2+32}=\varphi\smallskip\\\varphi=3\end{cases}\!\!\!\!\!\!\Leftrightarrow\sqrt[4]{x^2+32}=3\Leftrightarrow x^2+32=81\Leftrightarrow x^2=49\Leftrightarrow x\in\left\{-7;7\right\}")
Ответ. 