\( 1.1 .3 \quad x-4 \sqrt{x}+3=0 \)

The provided equation is not in the correct format. Let's rewrite the equation as \(x - 4\sqrt{x} + 3 = 0\) and then solve it. Solve the equation by following steps: - step0: Solve for \(x\): \(x-4\sqrt{x}+3=0\) - step1: Find the domain: \(x-4\sqrt{x}+3=0,x\geq 0\) - step2: Move the expression to the right-hand side: \(-4\sqrt{x}=-x-3\) - step3: Divide both sides: \(4\sqrt{x}=x+3\) - step4: Rewrite the expression: \(\sqrt{x}=\frac{x+3}{4}\) - step5: Evaluate: \(\sqrt{x}=\frac{x+3}{4},\frac{x+3}{4}\geq 0\) - step6: Evaluate: \(\sqrt{x}=\frac{x+3}{4},x\geq -3\) - step7: Solve the equation: \(\begin{align}&x=9\\&x=1\end{align},x\geq -3\) - step8: Find the intersection: \(\begin{align}&x=9\\&x=1\end{align}\) - step9: Check if the solution is in the defined range: \(\begin{align}&x=9\\&x=1\end{align},x\geq 0\) - step10: Find the intersection: \(\begin{align}&x=9\\&x=1\end{align}\) - step11: Check the solution: \(\begin{align}&x=9\\&x=1\end{align}\) - step12: Rewrite: \(x_{1}=1,x_{2}=9\) The solutions to the equation \(x - 4\sqrt{x} + 3 = 0\) are \(x = 1\) and \(x = 9\).