Question 443172
{{{(abc)^3 - 3abc = 0}}}
{{{abc((abc)^2 - 3)= 0}}}
Then we have abc = 0 
or  
{{{(abc)^2 = 3}}}
{{{(abc) = sqrt(3)}}}
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Suppose a = b = c

Then {{{ a^3 = sqrt(3)}}}
     {{{ a = root(3,sqrt(3))}}}
     
Plug this back in for a=b=c

and you get

{{{root(3,sqrt(3))^3 * root(3,sqrt(3))^3 * root(3,sqrt(3))^3 = 3*root(3,sqrt(3))^3}}}
{{{sqrt(3) * sqrt(3) * sqrt(3) = 3sqrt(3)}}}
{{{3*sqrt(3) = 3*sqrt(3)}}} Check.

Then {{{abc =0}}} or {{{a=b=c=root(3,sqrt(3))}}}