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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset Vaia Explanations$ Math

2nd Edition · 1240 pages

ISBN: 9780998625713

Chapter 10: Q 287 (page 1237)

Find two consecutive odd numbers whose product is 323 .

Short Answer

Expert verified

The two consecutive integers are $(- 19, - 17), (17, 19)$

Step by step solution

01

Given information

The product of two consecutive odd integer is 323.

02

Solve the equation

Let $n =$ the first odd integer

$n + 1 =$ the next odd integer.

The product of two consecutive odd integers is 323

The product of the first odd integer and the second odd integer is 323.

$(n) (n + 2) = 323 n^{2} + 2 n = 323 n^{2} + 2 n - 323 = 0$

03

Now , use quadratic formula to solve quadratic equation .

Identify the value of $a, b, c$

$a = 1, b = 2, c = - 323$

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

$n = \frac{- (2) \pm \sqrt{{(2)}^{2} - 4 (1) (- 323)}}{2 (1)} n = \frac{- 2 \pm \sqrt{4 + 1292}}{2} n = \frac{- 2 \pm \sqrt{1296}}{2} n = \frac{- 2 \pm 36}{2} n = \frac{- 2 - 36}{2}, \frac{- 2 + 36}{2} n = \frac{- 38}{2}, \frac{34}{2} n = - 19, 17$

When one number is $- 19$

Other consecutive number is $- 19 + 2 = - 17$

On the other hand when one number is $17$

Other consecutive number is $17 + 2 = 19$

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