Q. 316 - Intermediate Algebra

Question

In the following exercises, solve.

$\sqrt{y+4}-y+2=0$

Step-by-Step Solution

Answer

The solution of the given equation is $y=5$.

Step 1. Given information.

The given equation is:

$\sqrt{y+4}-y+2=0$

Step 2. Simplify the equation.

The given equation can be written as:

$\sqrt{y+4}=y-2$

Take square on both sides.

$\begin{array}{rcl}y+4& =& (y-2{)}^2\\ y+4& =& y^2-4y+4\\ 0& =& y^2-4y+4-y-4\\ 0& =& y^2-5y\end{array}$

Step 3. Solve the equation.

The above equation can be written as:

$\begin{array}{rcl}{y}^2-5y& =& 0\\ y(y-5)& =& 0\\ y& =& 0,5\end{array}$

For $y=0$,

$\sqrt{0+4}-0+2=4\ne 0$

For $y=5$,

$\sqrt{5+4}-5+2=0$

Step 4. Conclusion.

The solution of the given equation is $y=5$.