Question 167570
{{{3x^(3)y^(2)-3x^(2)y^(2)+3xy^(2)=3y^(2)(x^(3)-x^(2)+x)}}}
{{{3x^(3)y^(2)-3x^(2)y^(2)+3xy^(2)=3xy^(2)(x^(2)-x+1)}}}
Let's look at the roots of the quadratic equation using the quadratic formula,
{{{x^(2)-x+1=0}}}
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (-(-1) +- sqrt( (-1)^2-4*1*1 ))/(2*1) }}}
{{{x = (1 +- sqrt( 1-4 ))/(2) }}}  
{{{x = (1 +- sqrt( -3 ))/(2) }}} 
{{{x = (1 +- sqrt( 3 )i)/(2) }}} 
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{{{3x^(3)y^(2)-3x^(2)y^(2)+3xy^(2)=3xy^(2)(x^(2)-x+1)}}}
{{{3x^(3)y^(2)-3x^(2)y^(2)+3xy^(2)=3xy^(2)(x-(1+sqrt(3)i)/(2))(x-(1-sqrt(3)i)/(2))}}}