Q.461. Solve the given equation.x23-101... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q.461. (page 984)

Solve the given equation.
$x^{\frac{2}{3}} - 10^{\frac{1}{3}} + 24 = 0$

Short Answer

Expert verified

The solutions are $x = 64$ and $x = 216$ .

Step by step solution

Step 1. Given information.

The given equation is $x^{\frac{2}{3}} - 10^{\frac{1}{3}} + 24 = 0$ .

Step 2. Simplify the equation.

$\begin{array}{rcl} x^{\frac{2}{3}} - 10 x^{\frac{1}{3}} + 24 & = & 0 \\ {(x^{\frac{1}{3}})}^{2} - 10 x^{\frac{1}{3}} + 24 & = & 0 \\ {(x^{\frac{1}{3}})}^{2} - 6 x^{\frac{1}{3}} - 4 x^{\frac{1}{3}} + 24 & = & 0 \\ x^{\frac{1}{3}} (x^{\frac{1}{3}} - 6) - 4 (x^{\frac{1}{3}} - 6) & = & 0 \\ (x^{\frac{1}{3}} - 4) (x^{\frac{1}{3}} - 6) & = & 0 \end{array}$

Step 3. Solve the equation for x.

$\begin{array}{rcl} x^{\frac{1}{3}} - 6 & = & 0 \\ x^{\frac{1}{3}} & = & 6 \\ {(x^{\frac{1}{3}})}^{3} & = & 6^{3} \\ x & = & 216 \end{array}$ and $\begin{array}{rcl} x^{\frac{1}{3}} - 4 & = & 0 \\ x^{\frac{1}{3}} & = & 4 \\ {(x^{\frac{1}{3}})}^{3} & = & 4^{3} \\ x & = & 64 \end{array}$

Step 4. Simplified answer.

Hence, the required solutions are $x = 64$ and $x = 216$ .

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

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Solve the given equation.
$x^{\frac{2}{3}} - 10^{\frac{1}{3}} + 24 = 0$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

Step 3. Solve the equation for x.

Step 4. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Mechanics Maths

Logic and Functions

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

91影视

Solve the given equation.x23-1013+24=0

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

Step 3. Solve the equation for x.

Step 4. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Mechanics Maths

Logic and Functions

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

Solve the given equation.
$x^{\frac{2}{3}} - 10^{\frac{1}{3}} + 24 = 0$