Question

In the following exercises, solve.
$\sqrt{x+1}-x+1=0$

Short answer

The solution of the given equation is $x=3$.

Step-by-step solution

Step 1. Given information.

The given equation is:

$\sqrt{x+1}-x+1=0$

Step 2. Simplify the equation.

The given equation can be written as:

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

Take square on both sides.

$\begin{array}{rcl}x+1& =& (x-1{)}^2\\ x+1& =& x^2-2x+1\\ 0& =& x^2-2x+1-x-1\\ 0& =& x^2-3x\end{array}$

Step 3. Solve the equation.

The above equation can be written as:

$\begin{array}{rcl}{x}^2-3x& =& 0\\ x(x-3)& =& 0\\ x& =& 0,3\end{array}$

For $x=0$,

$\sqrt{0+1}-0+1=1\ne 0$

For $x=3$,

$\sqrt{3+1}-3+1=0$

Step 4. Conclusion.

The solution of the given equation is $x=3$.