Q. 333 - Intermediate Algebra

Question

In the following exercises, solve.
$\sqrt{u}+1=\sqrt{u+4}$

Step-by-Step Solution

Answer

The solution of the given equation is $u=\frac{9}{4}$.

Step 1. Given information.

The given equation is:

$\sqrt{u}+1=\sqrt{u+4}$

Step 2. Simplify the equation.

Take square on both sides.

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

Step 3. Solve the equation.

Isolate the variable.

$\begin{array}{rcl}u+2\sqrt{u}-u& =& 4-1\\ 2\sqrt{u}& =& 3\\ \sqrt{u}& =& \frac{3}{2}\\ u& =& {\left(\frac{3}{2}\right)}^2\\ u& =& \frac{9}{4}\end{array}$

Step 4. Conclusion.

The solution of the given equation is $u=\frac{9}{4}$.