Q. 337 - Intermediate Algebra

Question

In the following exercises, solve.

$\sqrt{2x+1}=1+\sqrt{x}$

Step-by-Step Solution

Answer

The solutions of the given equation are $x=0$ and $x=4$.

Step 1. Given information.

The given equation is:

$\sqrt{2x+1}=1+\sqrt{x}$

Step 2. Simplify the equation.

Take square on both sides.

$\begin{array}{rcl}(\sqrt{2x+1}{)}^2& =& (1+\sqrt{x}{)}^2\\ 2x+1& =& 1^2+2\left(1\right)\left(\sqrt{x}\right)+(\sqrt{x}{)}^2\\ 0& =& 2\sqrt{x}-x\\ x& =& 2\sqrt{x}\end{array}$

Step 3. Solve the equation.

Take square on both sides.

$\begin{array}{rcl}{x}^2& =& (2\sqrt{x}{)}^2\\ x^2& =& 4x\\ x^2-4x& =& 0\\ x(x-4)& =& 0\\ x& =& 0,4\end{array}$

Step 4. Conclusion.

The solutions of the given equation are $x=0$ and $x=4$.