Question

The sum of the squares of two numbers is 24 The difference of the squares of the numbers is $8 .$ Find the numbers.

Name: Problem 52, Chapter 9: Intermediate Algebra
Uploaded: 2020-06-30T06:25:17-08:00
Duration: 1 min 24 s
Channel: Ankit Gupta
Description: The sum of the squares of two numbers is 24 The difference of the squares of the numbers is 8 . Find the numbers.

   The sum of the squares of two numbers is 24 The difference of the squares of the numbers is $8 .$ Find the numbers.

Intermediate Algebra

Julie Miller, Molly… 5th Edition

Chapter 9, Problem 52

Instant Answer

Solved by Expert Ankit Gupta

06/30/2020

Step 1

The first equation is the sum of the squares of two numbers which is $x^2 + y^2 = 24$. The second equation is the difference of the squares of the numbers which is $x^2 - y^2 = 8$. Show more…

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The sum of the squares of two numbers is 24 The difference of the squares of the numbers is $8 .$ Find the numbers.

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Key Concepts

Quadratic Expressions

Quadratic expressions, which involve variables raised to the second power, are central to many algebra problems. Their properties, including how they combine in sums and differences, underpin techniques for solving equations and are crucial for understanding the behavior of parabolic functions.

System of Equations

A system of equations involves finding a set of values for variables that simultaneously satisfy all given equations. This concept is fundamental in algebra, as it allows the interrelation of different conditions, enabling one to isolate variables through substitution, elimination, or other algebraic techniques.

Difference of Squares

The difference of squares is a specific algebraic pattern expressed as a^2 - b^2, which factors into (a+b)(a-b). Recognizing this pattern is a key technique that simplifies complex equations by breaking them down into more manageable factors.

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