There is a very simple way to the solutions : write the equation as (x-1)^4=c^4*3^4 ,with c= ±1 or ± i.This implies x-1=c *3 ,or x= -2,4,1±3 i. An important point is that this method works for the general case (x-a)^n = b^n . Then one has the n solutions x (k) = a+ e^(2*π*i *k/n)*b , k= 0,1,2,....n-1.
There is a very simple way to the solutions : write the equation as (x-1)^4=c^4*3^4 ,with c= ±1 or ± i.This implies
x-1=c *3 ,or x= -2,4,1±3 i. An important point is that this method works for the general case (x-a)^n = b^n .
Then one has the n solutions x (k) = a+ e^(2*π*i *k/n)*b , k= 0,1,2,....n-1.