Solve the equations reducible to quadratic

Question

Solve the following equations:

(1) x³-3x²=4x



(2) x⁶-2x³-3=0

Answer 1

In the previous answer for this question, the factors for the first problem are incorrect.

The correct factors are

      x(x-4)(x+1)

Then,

      x-0 or x=4 or x=-1

Answer 2

First problem. 

               x^3 - 3x^2 = 4x

               x^3 - 3x^2 - 4x = 0 

               x(x^2 - 3x - 4) = 0 

 

Factor. 

 

               x(x-3)(x-1) = 0 

Then, 

               x = 0 or x = 3 or x = 1. 

 

Next problem. 

               x^6 - 2x^3 - 3 = 0 

Factor. 

               (x^3 - 3)(x^3 + 1) = 0 

Then, 

               x^3 - 3 = 0     or     x^3 + 1 = 0 

               x^3 = 3          or    x^3 = -1 

               x = 3^1/3       or    x = -1