Q. 301 - Intermediate Algebra

Question

In the following exercises, solve.
$\sqrt{u-3}-3=u$

Step-by-Step Solution

Answer

The given equation has no solution.

Step 1. Given information.

The given equation is:

$\sqrt{u-3}-3=u$

Step 2. Simplify the equation.

The given equation can be written as:

$\sqrt{u-3}=u+3$

Take square on both sides.

$\begin{array}{rcl}(\sqrt{u-3}{)}^2& =& (u+3{)}^2\\ u-3& =& u^2+6u+9\\ 0& =& u^2+6u+9-u+3\\ 0& =& u^2+5u+6\end{array}$

Step 3. Solve the equation.

The above equation can be written as:

$\begin{array}{rcl}{u}^2+3u+2u+6& =& 0\\ u(u+3)+2(u+3)& =& 0\\ (u+3)(u+2)& =& 0\\ u& =& -3,-2\end{array}$

For these values, the expression $\sqrt{u-3}$ is not defined. So, the given equation has no solution.

Step 4. Conclusion.

The given equation has no solution.