SOLUTION: If a^3 b^3 c^3=3abc show that either a b c=0 or a=b=c

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Question 443172: If a^3 b^3 c^3=3abc show that either a b c=0 or a=b=c
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
%28abc%29%5E3+-+3abc+=+0
abc%28%28abc%29%5E2+-+3%29=+0
Then we have abc = 0
or
%28abc%29%5E2+=+3
%28abc%29+=+sqrt%283%29
-------------------
Suppose a = b = c
Then +a%5E3+=+sqrt%283%29
+a+=+root%283%2Csqrt%283%29%29

Plug this back in for a=b=c
and you get

sqrt%283%29+%2A+sqrt%283%29+%2A+sqrt%283%29+=+3sqrt%283%29
3%2Asqrt%283%29+=+3%2Asqrt%283%29 Check.
Then abc+=0 or a=b=c=root%283%2Csqrt%283%29%29