$\sqrt{3-x}=\sqrt{x-3}+1_{}$
$⇔3-x=x-3+2\sqrt{x-3}+1_{}$
$⇔3-x=x-2+2\sqrt{x-3}_{}$
$⇔-2\sqrt{x-3}=x-2-3+x_{}$
$⇔-2\sqrt{x-3}=2x-5_{}$
$⇔4.(x-3)=4x^2-20x+25_{}$
$⇔4x-12=4x^2-20x+25_{}$
$⇔4x-12-4x^2+20x-25=0_{}$
$⇔24x-37-4x^2=0_{}$
$⇔-4x^2+24x-37=0_{}$
$⇔4x^2-24x+37=0_{}$ $x∈R_{}$
$Vậy_{}$ $pt_{}$ $vô_{}$ $nghiệm_{}$