<s>[INST] How can I solve this equation for real numbers? How can I solve this equation for real numbers?
$$(x+2)^4+x^4=82.$$
I tried $(x+2)^4+x^4-82=
2x^4 + 8 x^3 + 24 x^2 + 32 x - 66=0$
It is very difficult to continue.
 [/INST] Look my method:
Let $x+1=y$
$(y+1)^4+(y-1)^4=82 \Rightarrow y^4+6y^2-40=0 \Rightarrow$ $y^2=-10$ and $y^2=4$
Finally, $x_1=-3, x_2=-2$
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