Solve the equation x^6-4x^3+3=0

We have to solve x^6 - 4x^3 + 3 =
0

Let y = x^3

x^6 - 4x^3 + 3 =
0

=> y^2 - 4y + 3 =
0

=> y^2 - 3y - y + 3 =
0

=> y(y - 3) - 1(y - 3) =
0

=> (y - 1)(y-3) =
0

We get y = 1 and y = 3

Now y
= x^3

Therefore we have

x^3 =
1 => x = 1^(1/3) = 1

x^3 = 3 => x = 3^(1/3) =
cube root 3

The values are:

x = 1

x = cube root
3