Chapter 1 - Section 1.4 - Radical Equations; Equations Quadratic in Form; Factorable Equations - 1.4 Assess Your Understanding - Page 118: 33

$x=1$

$\sqrt{3-2\sqrt{x}}=\sqrt x\\(\sqrt{3-2\sqrt{x}})^2=(\sqrt x)^2\\3-2\sqrt{x}=x\\3-x=2\sqrt{x}\\(3-x)^2=(2\sqrt{x})^2\\9+x^2-6x=4x\\x^2-10x+9=x^2-x-9x+9=x(x-1)-9(x-1)=(x-1)(x-9)=0$ Thus $x=1$ or $x=9$ but the equation is undefined for the latter, thus $x=1$.