Q. 334 - Intermediate Algebra

Question

In the following exercises, solve.
$\sqrt{x}+1=\sqrt{x+2}$

Step-by-Step Solution

Answer

The solution of the given equation is $x=\frac{1}{4}$.

Step 1. Given information.

The given equation is:

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

Step 2. Simplify the equation.

Take square on both sides.

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

Step 3. Solve the equation.

Isolate the variable.

$\begin{array}{rcl}x+2\sqrt{x}-x& =& 2-1\\ 2\sqrt{x}& =& 1\\ \sqrt{x}& =& \frac{1}{2}\\ x& =& {\left(\frac{1}{2}\right)}^2\\ x& =& \frac{1}{4}\end{array}$

Step 4. Conclusion.

The solution of the given equation is $x=\frac{1}{4}$.