Giaiiphuougtrinh sau: $$ \sqrt{2 x-1}+\sqrt{x+3}: 3 $$

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Solve the equation $$ \sqrt{2x-1}+\sqrt{x+3}=3 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\sqrt{2x-1}+\sqrt{x+3}=3$$
- step1: Find the domain:
  $$\sqrt{2x-1}+\sqrt{x+3}=3,x\geq \frac{1}{2}$$
- step2: Move the expression to the right-hand side:
  $$\sqrt{2x-1}=3-\sqrt{x+3}$$
- step3: Evaluate:
  $$\sqrt{2x-1}=3-\sqrt{x+3},3-\sqrt{x+3}\geq 0$$
- step4: Evaluate:
  $$\sqrt{2x-1}=3-\sqrt{x+3},x\leq 6$$
- step5: Solve the equation:
  $$x=1,x\leq 6$$
- step6: Find the intersection:
  $$x=1$$
- step7: Check if the solution is in the defined range:
  $$x=1,x\geq \frac{1}{2}$$
- step8: Find the intersection:
  $$x=1$$
- step9: Check the solution:
  $$x=1$$
The solution to the equation $$ \sqrt{2x-1}+\sqrt{x+3}=3 $$ is $$ x=1 $$.
$$ x=1 $$

Giaiiphuougtrinh sau:

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