Задание 3029

Больше разборов вы найдете на моем ютуб-канале! Не забудьте подписаться!

$$(x+2)^{4}+(x+4)^{4}=82\Leftrightarrow$$ $$(x+2)^{4}+(x+4)^{4}=1^{4}+3^{4}\Leftrightarrow$$ $$\left\{\begin{matrix}\left[\begin{matrix}\left | x+2 \right |=1\\\left | x+4 \right |=3\end{matrix}\right. (1)\\\left[\begin{matrix}\left | x+2 \right |=3\\\left | x+4 \right |=1\end{matrix}\right. (2)\end{matrix}\right.$$

1) $$\left\{\begin{matrix}\left[\begin{matrix}x+2=1\\x+2=-1\end{matrix}\right.\\\left[\begin{matrix}x+4=3\\x+4=-3\end{matrix}\right.\end{matrix}\right.\Leftrightarrow$$ $$\left\{\begin{matrix}\left[\begin{matrix}x=-1\\x=-3\end{matrix}\right.\\\left[\begin{matrix}x=-1\\x=-7\end{matrix}\right.\end{matrix}\right.\Leftrightarrow x=-1$$

2) $$\left\{\begin{matrix}\left[\begin{matrix}x+2=3\\x+2=-3\end{matrix}\right.\\\left[\begin{matrix}x+4=1\\x+4=-1\end{matrix}\right.\end{matrix}\right.\Leftrightarrow$$ $$\left[\begin{matrix}\left\{\begin{matrix}x=1\\x=-5 \end{matrix}\right.\\\left[\begin{matrix}x=-3\\x=-5 \end{matrix}\right.\end{matrix}\right.\Leftrightarrow x=-5$$