Q. 11.78 The difference of the squares of... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 11.78 (page 1145)

The difference of the squares of two numbers is 35. The sum of the numbers is $- 1$ . Find the numbers.

Short Answer

Expert verified

The numbers are $17, - 18$ .

Step by step solution

Step 1. Given Information

The difference of the squares of two numbers is 35.
The sum of the numbers is $- 1$ .

Step 2. Form Equations

Assume that the numbers are x,y.
Their sum is $- 1$ . So, $x + y = - 1$
Difference of their square is 35. So, $x^{2} - y^{2} = 35$ .

Step 3. Substitute value from one equation to other

Simplify the first equation for x.

$x = - 1 - y$

Substitute this value into the second equation and solve for y.

$\begin{array}{rcl} {(- 1 - y)}^{2} - y^{2} & = & 35 \\ 1 + 2 y & = & 35 \\ 2 y & = & 34 \\ y & = & 17 \end{array}$

Step 4. Solve for x

Substitute $y = 17$ into $x + y = - 1$ and solve for x.

$\begin{array}{rcl} x + 17 & = & - 1 \\ x & = & - 18 \end{array}$

So, the numbers are $17, - 18$ .

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91影视

The difference of the squares of two numbers is 35. The sum of the numbers is $- 1$ . Find the numbers.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Form Equations

Step 3. Substitute value from one equation to other

Step 4. Solve for x

One App. One Place for Learning.

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91影视

The difference of the squares of two numbers is 35. The sum of the numbers is -1. Find the numbers.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Form Equations

Step 3. Substitute value from one equation to other

Step 4. Solve for x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Decision Maths

Mechanics Maths

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

The difference of the squares of two numbers is 35. The sum of the numbers is $- 1$ . Find the numbers.