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

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UpStudy AI · Accepted Answer

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 $$x = 9$$.
The solutions are $$x = 1$$ and $$x = 9$$.

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