Chapter 10: Q 288. (page 1237)

In the following exercises, solve by using methods of factoring, the square root principle, or the quadratic formula.
Find two consecutive even numbers whose product is 624.

Short Answer

Expert verified

The pair consecutive numbers are $- 24, - 26 a n d 24, 26 .$

Step by step solution

Given information.

The given statement is:

Find two consecutive even numbers whose product is 624.

Set up an equation so that the product of two even consecutive numbers is 624.

Let the first even number be $x .$

So, the next even number be $(x + 2) .$

$x (x + 2) = 624 x^{2} + 2 x = 624 x^{2} + 2 x - 624 = 0$

Solve for the value of x.

Factor the left side of the equation as $(x + 26) (x - 24) = 0$

Now apply the zero product property.

$(x + 26) = 0 x = - 26 A n d (x - 24) = 0 x = 24$

So, the first pair of consecutive numbers are $- 26 a n d - 26 + 2 = - 24 .$ The second pair of consecutive numbers are $24 a n d 24 + 2 = 26 .$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, solve by using methods of factoring, the square root principle, or the quadratic formula.
Find two consecutive even numbers whose product is 624.

Short Answer

Step by step solution

Given information.

Set up an equation so that the product of two even consecutive numbers is 624.

Solve for the value of x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve by using methods of factoring, the square root principle, or the quadratic formula.Find two consecutive even numbers whose product is 624.

Short Answer

Step by step solution

Given information.

Set up an equation so that the product of two even consecutive numbers is 624.

Solve for the value of x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve by using methods of factoring, the square root principle, or the quadratic formula.
Find two consecutive even numbers whose product is 624.