Question 1051781
{{{x-2=-x^2+4x-3}}}
{{{x^2-3x+1=0}}}
{{{x^2-3x+(3/2)^2+1=(3/2)^2}}}
{{{(x-3/2)^2=(3/2)^2-1}}}
{{{(x-3/2)^2=9/4-4/4}}}
{{{(x-3/2)^2=5/4}}}
{{{x-3/2=0 +- sqrt(5)/2}}}
{{{x=3/2 +- sqrt(5)/2}}}
{{{x=(3+-sqrt(5))/2}}}
and correspondingly,
{{{y=(-1+- sqrt(5))/2}}}
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*[illustration dfc7.JPG].