THE 2002 VIETNAMESE MATHEMATICAL OLYMPIAD

The set of definition of the equation is $X=[74/27;10/3]$. On $X$, we have: $$\begin{gathered} \text{given equation}\iff 4-3\sqrt{10-3x}=x^2-4x+4\iff 9(10-3x)=x^2(4-x{)}^2\iff \\ {x}^4-8x^3+16x^2+27x-90=0\iff (x-3)(x+2)(x^2-7x+15)=0\iff x=3. \end{gathered}$$