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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 337 (page 824)

In the following exercises, solve.
$\sqrt{2 x + 1} = 1 + \sqrt{x}$

Short Answer

Expert verified

The solutions of the given equation are $x = 0$ and $x = 4$ .

Step by step solution

01

Step 1. Given information.

The given equation is:

$\sqrt{2 x + 1} = 1 + \sqrt{x}$

02

Step 2. Simplify the equation.

Take square on both sides.

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

03

Step 3. Solve the equation.

Take square on both sides.

$\begin{array}{rcl} x^{2} & = & (2 \sqrt{x})^{2} \\ x^{2} & = & 4 x \\ x^{2} - 4 x & = & 0 \\ x (x - 4) & = & 0 \\ x & = & 0, 4 \end{array}$

04

Step 4. Conclusion.

The solutions of the given equation are $x = 0$ and $x = 4$ .

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