SOLUTION: a. Find all real solutions to: x^(2/3) - x^(1/3) = 6. If you elimate a solution or equation, explain or show why. State clearly any substitution used. b. A function f has the ve

Algebra ->  Equations -> SOLUTION: a. Find all real solutions to: x^(2/3) - x^(1/3) = 6. If you elimate a solution or equation, explain or show why. State clearly any substitution used. b. A function f has the ve      Log On


   

Question 948291: a. Find all real solutions to: x^(2/3) - x^(1/3) = 6. If you elimate a solution or equation, explain or show why. State clearly any substitution used.
b. A function f has the verbal description "Subtract 2, then cube the result" Find a formula that expresses f algebraically.
Thank you
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a)
Use a substitution, u=x%5E%281%2F3%29, u%5E2=x%5E%282%2F3%29
So,
u%5E2-u=6
u%5E2-u-6=0
%28u-3%29%28u%2B2%29=0
Two solutions:
u-3=0
u=3
x%5E%281%2F3%29=3
x=27
and
u%2B2=0
u=-2
x%5E%281%2F3%29=-2
x=-8
.
.
.
b) f%28x%29=%28x-2%29%5E3