/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 22 Solve each radical equation in C... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 22

Solve each radical equation in Check all proposed solutions. $$ \sqrt{x+5}-\sqrt{x-3}=2 $$

Short Answer

Expert verified
The solution to the equation is \(x = \frac{49}{16}\).

Step by step solution

01

Isolate one of the square roots

First, let's isolate one of the square roots. Let us isolate \(\sqrt{x+5}\) by adding \(\sqrt{x-3}\) on both sides of the equation. We get: \(\sqrt{x+5} = 2 + \sqrt{x-3}\)
02

Square both sides of the equation

Square both sides of the equation to eliminate the square root on the left-hand side. This gives us: \((\sqrt{x+5})^2 = (2 + \sqrt{x-3})^2\), which simplifies to: \(x + 5 = 4 + 4\sqrt{x-3} + x - 3\)
03

Simplify the equation

Next, simplify the equation by subtracting \(x\) and \(4\) from both sides. This results in: \(1 = 4\sqrt{x-3}\)
04

Isolate the remaining square root

Divide both sides of the equation by 4. This will isolate the remaining square root on the right-hand side: \(\frac{1}{4} = \sqrt{x-3}\)
05

Square both sides of the equation again

Squaring both sides of the equation will eliminate the square root on the right-hand side. This gives us: \(\left(\frac{1}{4}\right)^2 = (\sqrt{x-3})^2\), which simplifies to: \(\frac{1}{16} = x - 3\)
06

Solve for x

Add 3 to both sides of the equation to isolate \(x\): \(x = \frac{1}{16} + 3 = \frac{49}{16}\)
07

Check the solution

Finally, substitute \(x = \frac{49}{16}\) back into the original equation to confirm that it's a solution. \(\sqrt{\frac{49}{16} + 5} - \sqrt{\frac{49}{16} - 3}\) equals \(2\), so the solution is valid.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{x}{x+2} \geq 2 $$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ -x^{2}+2 x \geq 0 $$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$\sqrt{-64}-\sqrt{-25}$$

What is the complex conjugate of \(2+3 i ?\) What happens when you multiply this complex number by its complex conjugate?

In Exercises \(1-8,\) add or subtract as indicated and write the result in standard form. $$8 i-(14-9 i)$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.