Chapter 8: Q. 301 (page 824)

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

Short Answer

Expert verified

The given equation has no solution.

Step by step 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.

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

Step 3. Solve the equation.

The above equation can be written as:

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

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.

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

Step 3. Solve the equation.

Step 4. Conclusion.

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In the following exercises, solve.u-3-3=u

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

Step 3. Solve the equation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Mechanics Maths

Logic and Functions

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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