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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 228 (page 1148)

The sum of two numbers is 鈭�6 and the product is 8. Find the numbers.

Short Answer

Expert verified

If the first number is $- 2$ , then the second number is $- 4$ .

If the first number is $- 4$ , then the second number is $- 2$ .

Step by step solution

01

Step 1. Given information.

The value of the sum of two numbers is $- 6$ and the product of the two numbers is 8.

02

Step 2. Forming the equations.

Let the two numbers be $x$ and $y$ .

The sum of the two numbers is $- 6$ . In equation form, we can write this as

$x + y = - 6 - - - > (1)$

The product of the two numbers is 8. In equation from, we can write this as

$x y = 8 - - - > (2)$

03

Step 3. Solving the equations.

Solving equation (2) for $x$ :

$x = \frac{8}{y}$

Substituting this in the first equation, we get that

$\frac{8}{y} + y = - 6$

Multiplying both sides by $y$ and simplifying:

$8 + y^{2} = - 6 y y^{2} + 6 y + 8 = 0 y^{2} + 4 y + 2 y + 8 = 0 (y + 4) (y + 2) = 0 - - - > (3)$

When $y + 4 = 0$ , then $y = - 4$ .

In that case,

$x = - 6 - y = - 6 - (- 4) x = - 2$

When $y + 2 = 0$ , then $y = - 2$ .

In that case,

$x = - 6 - y = - 6 + 2 x = - 4$

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Most popular questions from this chapter

In the following exercises, factor the greatest common factor from each polynomial.

$- 6 a^{3} b - 12 a^{2} b^{2} + 18 a b^{2}$

Simplify the rational expression $\frac{3 m^{2} + 30 m n + 75 n^{2}}{4 m^{2} - 100 n^{2}}$

In the following exercises, multiply. $(\sqrt{3} + \sqrt{10}) (\sqrt{3} + 2 \sqrt{10})$

Simplify each expression:

$鈸� \frac{y^{43}}{y^{37}} 鈸� \frac{10^{15}}{10^{7}} 鈸� \frac{m^{7}}{m^{15}} 鈸� \frac{9^{8}}{9^{19}}$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{n^{21}}, \sqrt[3]{q^{8}}, \sqrt[8]{n^{10}}$

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