[tex]\sqrt{3-x}-\sqrt{2-x}=1\\
C.E. \left \{ {{3-x \geq 0} \atop {2-x \geq 0}} \right. \\
\sqrt{3-x}-\sqrt{2-x}=1\\
ridicam\:la\:patrat\\
(\sqrt{3-x}-\sqrt{2-x})^2=1\\
(\sqrt{3-x})^2-2\sqrt{3-x}\cdot\sqrt{2-x}+(\sqrt{2-x})^2=1\\
3-x-2\sqrt{(3-x)(2-x)}+2-x=1\\
5-2x-2\sqrt{(3-x)(2-x)}=1\\
-2\sqrt{(3-x)(2-x)}=1-5+2x\\
-2\sqrt{(3-x)(2-x)}=-4+2x\\
\sqrt{(3-x)(2-x)}=2-x\\
ridicam\:la\:patrat\\
(3-x)(2-x)=(2-x)^2\\
6-3x-2x+x^2=4-4x+x^2\\
6-5x+x^2=4-4x+x^2\\
6-5x=4-4x\\
x=2\:verifica\:C.E.
[/tex]
