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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 546 (page 988)

Find two consecutive even numbers whose product is $360 .$

Short Answer

Expert verified

The two consecutive even numbers that has the product of $360$ are $18$ androle="math" localid="1645438666037" $20$ or $- 18$ and $- 20$ .

Step by step solution

01

Step 1. Given information.

Two consecutive even numbers that has a product of $360 .$

02

Step 2. Make quadratic equation.

Let $x$ represent the first even number and let $x + 2$ represent the next even number.

When the two even number $x$ and $x + 2$ are multiplied, the answer is $360$ . It follows:

$x (x + 2) = 360 x^{2} + 2 x = 360 x^{2} + 2 x - 360 = 360 - 360 x^{2} + 2 x - 360 = 0$

03

Step 3. Solve the equation.

For a quadratic equation of the form $a x^{2} + b x + c = 0,$ the solutions are:

$x_{1, 鈥� 2} = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a} For 鈥� a = 1, 鈥� b = 2, 鈥� c = - 360 x_{1, 鈥� 2} = \frac{- 2 卤 \sqrt{2^{2} - 4 路鈥� 1 路 (- 360)}}{2 路鈥� 1} x_{1, 鈥� 2} = \frac{- 2 卤鈥� 38}{2 路鈥� 1} x = 18, 鈥� x = - 20$

When $x = 18$ :

$x + 2 = 18 + 2 = 20$

When $x = - 20 :$

$x + 2 = - 20 + 2 = - 18$

Therefore, the even numbers are:

$18$ and $20$

$- 18$ and $- 20$

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