Chapter 11: Q. 72 (page 774)

The sum of two numbers is $7$ , and the difference of their
squares is $21$ . Find the numbers.

Short Answer

Expert verified

The required numbers are, $5, 2$ .

Step by step solution

Step 1. Given information

Given that,

The sum of two numbers is $7$ . So, $a + b = 7$ .

The difference of their squares is $21$ . So, $a^{2} - b^{2} = 21$ .

So, the system of equations are,

$\{\begin{cases} a + b = 7 \\ a^{2} - b^{2} = 21 \end{cases}$

Step 2 Let us write the first equation as,

$a = 7 - b$ .

Substitute the value of $a$ in the second equation.

${(7 - b)}^{2} - b^{2} = 21 7^{2} - 14 b + b^{2} - b^{2} = 21 49 - 14 b = 21 14 b = 28 b = 2$

Step 3 Now substitute the value of b in the first equation.

$a + 2 = 7 a = 7 - 2 a = 5$

So, the required numbers are, $5, 2$ .

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The sum of two numbers is $7$ , and the difference of their
squares is $21$ . Find the numbers.

Short Answer

Step by step solution

Step 1. Given information

Step 2 Let us write the first equation as,

Step 3 Now substitute the value of b in the first equation.

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The sum of two numbers is 7, and the difference of theirsquares is 21. Find the numbers.

Short Answer

Step by step solution

Step 1. Given information

Step 2 Let us write the first equation as,

Step 3 Now substitute the value of b in the first equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Decision Maths

Statistics

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

The sum of two numbers is $7$ , and the difference of their
squares is $21$ . Find the numbers.