+118608 1 + x + x^2 + x^3 = x^4 + x^5.
\(1 + x + x^2 + x^3 - x^4 - x^5.=0\\ (1+x)+x^2(1+x)-x^4(1+x)=0\\ (1+x)(1+x^2-x^4)=0\\ \text{one solution is x=-1}\\ Consider\;\; \\ 1+x^2-x^4=0\\ x^4-x^2-1=0\\ x^2=\frac{1\pm \sqrt{1+4}}{2}\\ x^2 \text{ can't be negative so}\\ x^2=\frac{1+ \sqrt{5}}{2}\\ x=\pm \sqrt{\frac{1+ \sqrt{5}}{2}}\;\;or\;\;-1 \)
So I get 3 solutions same as EP.
But I have not checked if my irrational ones are the same as his, I assum that they are.
