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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 229 (page 1148)

The sum of two numbers is 11 and the product is −42. Find the numbers.

Short Answer

Expert verified

$- 3$ and 14.

Step by step solution

01

Step 1. Given information.

The sum of two numbers is 11 and the product of the two numbers is -42.

02

Step 2. Forming and solving the equations.

Let $x$ be the first number and $y$ be the second number.

According to the given information, we have

$x + y = 11 - - - > (1) x . y = - 42 - - - > (2)$

From equation (2), solving for $x$ :

$x = - \frac{42}{y} - - - > (3)$

Substituting this in equation (1) gives

$- \frac{42}{y} + y = 11$

Multiplying both sides by $y$ and simplifying

role="math" $- 42 + y^{2} = 11 y y^{2} - 11 y - 42 = 0$

Factor the quadratic equation:

$y^{2} - 14 y + 3 y - 42 = 0 (y - 14) (y + 3) = 0$

If $(y - 14) = 0$ , then $y = 14$ and $x = 11 - 14 = - 3$ .

If $(y + 3) = 0$ , then $y = - 3$ and then $x = 11 - (- 3) = 14$

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