/*! 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 131 Determine whether each statement... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 131

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. To solve \(x-9 \sqrt{x}+14=0,\) we let \(\sqrt{u}=x\)

Short Answer

Expert verified
The statement is false. The correct substitution is \(u = \sqrt{x}\) and the corrected equation should be \(u^2-9u+14=0\). Solving this equation gives us the solutions for \(x\) as 4 and 49.

Step by step solution

01

Analyze the statement

The given equation is \(x-9 \sqrt{x}+14=0\), and it's suggested that we let \(\sqrt{u}=x\). However, if we want to eradicate the square root from the equation, the correct substitution would be to let \(u\) substitute \(\sqrt{x}\), not \(\sqrt{u}\). So, let \(u = \sqrt{x}\) or \(x = u^2\). Therefore from this we can conclude that the original statement is false.
02

Substitute the correct variable

We should substitute \(x = u^2\) into the given equation to get rid of the square root. So after substitution, the equation would be: \(u^2-9u+14=0\).
03

Validate the work

Solving the quadratic equation \(u^2-9u+14=0\) will give the values of \(u\). Using the quadratic formula, i.e., \(u = \frac{-b\pm \sqrt{b^2-4ac}}{2a}\) yields the values \(u = 2\) and \(u = 7\). Keep in mind that \(u\) is the square root of \(x\), so \(x = u^2\), and substituting \(2^2\) and \(7^2\) into \(x\) will yield 4 and 49 respectively. These are valid solutions to the equation.

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 formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$C=2 \pi r \text { for } r$$

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$D=R T \quad \text{for} \quad R$$

The length of a rectangular pool is 6 meters less than twice the width. If the pool's perimeter is 126 meters, what are its dimensions?

Use the Pythagorean Theorem and the square root property to solve Exercises \(140-143 .\) Express answers in simplified radical form. Then find a decimal approximation to the nearest tenth. The base of a 30 -foot ladder is 10 feet from a building. If the ladder reaches the flat roof, how tall is the building?

In Exercises \(115-122,\) find all values of \(x\) satisfying the given conditions. $$ y_{1}=\frac{3}{x-1}, y_{2}=\frac{8}{x}, \text { and } y_{1}+y_{2}=3 $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Logic and Functions

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.