<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] $$u=x+1$$
$$(u+1)^4+(u-1)^4=82$$
$$u^4+4u^3+6u^2+4u+1+u^4-4u^3+6u^2-4u+1=82$$
$$2u^4+12u^2=80$$
$$u^4+6u^2-40=0$$
$$(u^2+10)(u^2-4)=0$$
$$u^2=4$$
$$u=\pm2$$
$$x=-3\lor x=1$$
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