Q. 303 - Intermediate Algebra

Question

In the following exercises, solve.
$\sqrt{r-1}=r-1$

Step-by-Step Solution

Answer

The solutions of the given equation are $r=1$ and $r=2$.

Step 1. Given information.

The given equation is:

$\sqrt{r-1}=r-1$

Step 2. Solve the equation.

Take square on both sides.

$\begin{array}{rcl}(\sqrt{r-1}{)}^2& =& (r-1{)}^2\\ r-1& =& (r-1{)}^2\\ 0& =& (r-1{)}^2-(r-1)\\ 0& =& (r-1)(r-1-1)\\ 0& =& (r-1)(r-2)\\ r& =& 1,2\end{array}$

Step 3. Conclusion.

The solutions of the given equation are $r=1$ and $r=2$.