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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 232 (page 1148)

The difference of the squares of two numbers is 15. The difference of twice the square of the first number and the square of the second number is 30. Find the numbers.

Short Answer

Expert verified

3.873 and 0 or -3.873 and 0

Step by step solution

01

Step 1. Given information.

The difference between the squares of the two numbers is 15. Also, the difference between twice the square of the first number and the square of the second number is 30.

02

Step 2. Forming the equations.

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

From the given conditions, we can form the following equations:

$x^{2} - y^{2} = 15 - - - > (1) 2 x^{2} - y^{2} = 30 - - - > (2)$

03

Step 3. Solving the equations.

Solving equation (1) for $x^{2}$ gives

$x^{2} = 15 + y^{2}$

Substituting this in equation (2):

$2 (15 + y^{2}) - y^{2} = 30 30 + 2 y^{2} - y^{2} = 30 y^{2} = 0$

Solving for $y$ , we get that

$y = 0$

From equation (1)

$x^{2} = 15 - 0 x = \pm \sqrt{15} x = \pm 3.873$

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Most popular questions from this chapter

Simplify the complex rational expression by writing it as division:

$\frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{a^{2}} - \frac{1}{b^{2}}}$

Simplify the complex rational expression by LCD:

$\frac{\frac{1}{4} + \frac{3}{8}}{\frac{1}{2} - \frac{5}{16}}$

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

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

In the following exercises, find the function values for each polynomial function.

For the function $f (x) = 5 x^{2} - x - 7$ , find:

(a) f(-4) (b) f(1) (c) f(0)

Simplify

(a) ${(\frac{1}{2} y^{2})}^{3} {(\frac{2}{3} y)}^{2}$

(b) ${(\frac{1}{2} j^{2})}^{5} {(\frac{2}{5} j^{3})}^{2}$

See all solutions

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