SOLUTION: Solve the equation. 6x^(-1/2) - 13x^(-1/4) +6 = 0

Algebra ->  Expressions-with-variables -> SOLUTION: Solve the equation. 6x^(-1/2) - 13x^(-1/4) +6 = 0      Log On


   



Question 270066: Solve the equation.

6x^(-1/2) - 13x^(-1/4) +6 = 0

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equation.
6x^(-1/2) - 13x^(-1/4) +6 = 0
----
Let x^(-1/4) = w
------
You get the quadratic:
6w^2 - 13w + 6 = 0
---
6w^2 -4w-9w + 6 = 0
----
2w(3w-2) -3(3w-2) = 0
Factor:
(3w-2)(2w-3) = 0
-------
w= 2/3 or w = 3/2
------------------------
Now solve for "x":
If x = 2/3
x^(-1/4) = 2/3
x = (2/3)^(-4)
x = 81/16
------
If w = 3/2
x^(-1/4) = 3/2
x = (3/2)^-4
x = 16/81
================
Cheers,
Stan H.