- #1
Doubell
- 29
- 0
Homework Statement
SOLVE FOR X IN THE EQUATION:
X^(1/3) - 4(X^[-1/3]) = 3
Homework Equations
The Attempt at a Solution
I LET X^1/3 = Y
THEN THE ORIGINAL EQUATION BECOMES
Y - 4* 1/Y = 3
MULTIPLYING THE ENTIRE EQUATION BY Y RESULTS IN
Y^2 - 4 = 3Y
THEREFORE Y^2 -3Y - 4 = 0
THE ROOTS OF THE EQUATION ARE DEFINED BY (Y+1) (Y-4)
THEREFORE Y = -1 OR Y = 4
AND SINCE Y = X^1/3 THEN
X^1/3 = -1 OR X^1/3 = 4
THEREFORE [X^1/3]^3 = [-1]^3 SO X = -1 AND [X^1/3]^3 = [4]^3 SO X = 64
HENCE THE SOLUTIONS OF X ARE -1 AND 64.