Question 427393
Solution:First we factor the function:

{{{(x^4-1)-4x(x^2-1)}}}=

{{{(x^2-1)*(x^2+1)-4x(x^2-1)}}}=

{{{(x^2-1)*(x^2+1-4x)}}}=

{{{(x-1)(x+1)(x^2-4x+1)}}} To find all the zeros equalize to zero all the factors:

x-1=0 => x=1; x+1=0 => x=-1;

{{{x^2-4x+1=0}}} =>

{{{x=2+- sqrt(3)}}}

The solution set of this function is:{-1, 1, 2+-sqrt(3)}

{{{graph(400, 400, -5, 5, -16, 5, x^4-4x^3+4x-1)}}}