SOLUTION: Solve the cubic equations: a) (x - 3)^2 = 4/x b) x(x+3)(x-1) = x + 8 c) x^3 + 4 = x(x + 4)

Algebra ->  Square-cubic-other-roots -> SOLUTION: Solve the cubic equations: a) (x - 3)^2 = 4/x b) x(x+3)(x-1) = x + 8 c) x^3 + 4 = x(x + 4)       Log On


   

Question 389390: Solve the cubic equations:
a) (x - 3)^2 = 4/x
b) x(x+3)(x-1) = x + 8
c) x^3 + 4 = x(x + 4)
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,            

a) (x - 3)^2 = 4/x  OR x^3 -6x^2 + 9x - 4 = 0  where x = 1 is one solution

     Applying division process:

     ____________________

x -1 |x^3 -6x^2 + 9x - 4     =    x^2 - 5x  + 4 

 (x-1)(x-4)(x-1)  = 0   x = {1,4}

b) x(x+3)(x-1) = x + 8  OR x^3 + 2x^2 -4x -8= 0  where x= 2 is one solution

  Applying division process:

      ___________________

x -2 |x^3 + 2x^2 -4x -8      = x^2 - 4

 (x-2)(x-2)(x+2) = 0   x = { 2, -2}

c) x^3 + 4 = x(x + 4)  OR x^3 - x^2 - 4x + 4  where x = 1 is one solution

   Applying division process:

     ___________________

x -1 |x^3 - x^2 - 4x + 4     = x^2 - 4

 (x-1)(x-2)(x+2)   x = {1,2,-2}