# Task 4. (12 points)

Solve the equation $(x+2)^{4}+x^{4}=82$.

#
# Solution

Let $y=x+1$, then we get

$$
(y+1)^{4}+(y-1)^{4}=82 \Leftrightarrow y^{4}+6 y^{2}-40=0 \Leftrightarrow\left[\begin{array} { l } 
{ y ^ { 2 } = - 1 0 } \\
{ y ^ { 2 } = 4 }
\end{array} \Rightarrow \left[\begin{array}{l}
x=-3 \\
x=1
\end{array}\right.\right.
$$

$\underline{\text { Answer: }} x_{1}=-3 ; x_{2}=1$.