SOLUTION: X 2/3 - X 1/3-6=0

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Question 59242: X 2/3 - X 1/3-6=0
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
X%5E%282%2F3%29-X%5E%281%2F3%29-6=0 Let X%5E1%2F3=p
%28X%5E%281%2F3%29%29%5E2-%28X%5E%281%2F3%29%29-6=0
p%5E2-p-6=0 Factor as usual.
%28p-3%29%28p%2B2%29=0
p-3=0 and p+2=0
p=3 and p=-2 But we want to know what X is, so let p=X%5E%281%2F3%29 again.
X%5E%281%2F3%29=3 and X%5E%281%2F3%29=-2
%28X%5E%281%2F3%29%29%5E3=3%5E3 and %28X%5E%281%2F3%29%29%5E3=%28-2%29%5E3
highlight%28X=27%29 and highlight%28X=-8%29
Check by substitution:
%2827%29%5E%282%2F3%29-%2827%29%5E%281%2F3%29-6=0
%283%5E3%29%5E%282%2F3%29-%283%5E3%29%5E%281%2F3%29-6=0
3%5E%286%2F3%29-3%5E%283%2F3%29-6=0
3%5E2-3-6=0
9-3-6=0
0=0 27 checks out
%28-8%29%5E%282%2F3%29-%28-8%29%5E%281%2F3%29-6=0
%28%28-2%29%5E3%29%5E%282%2F3%29-%28%28-2%29%5E3%29%5E%281%2F3%29-6=0
%28-2%29%5E%286%2F3%29-%28-2%29%5E%283%2F3%29-6=0
%28-2%29%5E2-%28-2%29-6=0
4%2B2-6=0
0=0 -8 checks too
Happy Calculating!!!