# 4. CONDITION

Find the real solutions of the equation $(x+2)^{4}+x^{4}=82$.

Hint. Let $x+1=y$, then $(y+1)^{4}+(y-1)^{4}=82$, or

$$
y^{4}+6 y^{2}-40=0 \text {, hence } y^{2}=-10 \text { or } y^{2}=4 \text {. }
$$