Solve the equation after making an appropriate substitution:

Question

√x -2 4√x-8 = 0 

 

Determine the appropriate substitution using the new u: u=

 

Write the new quadratic equation using the variable u:

 

Solve the new quadratic equation for variable u. u =

 

The solution set the original equation is { }      

Answer 1

With the clarification  that the equation is   x^1/2 - 2  x^1/4 - 8 = 0

 

 

the substitution u = x^1/4     will work.   The u equation becomes:   u² - 2 u - 8 =0

    This factors as   (u-4) (u + 2) = 0   So   u = 4  or  u = -2. 

 

However, u is the fourth root of something, so should be positive.   Hence u = 4 is the only solution.

 

  With u = 4,      x =  256  and the solution set   is  {256}