Question 379014
{{{sqrt( x) + sqrt(x-3) =0}}}
{{{sqrt( x) =- sqrt(x-3)}}}
{{{x=x-3}}}
{{{0=-3}}}
Yes, you are correct, there is no solution.
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Graphical verification.
As you can see the graph of {{{y=sqrt(x)+sqrt(x-3)}}} never crosses the x-axis.
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{{{graph(300,300,-2,18,-10,10,0,sqrt(x)+sqrt(x-3))}}}