(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

SOLVE FOR X IN THE EQUATION:

X^(1/3) - 4(X^[-1/3]) = 3

2. Relevant equations

3. 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.

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