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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

01

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, a2-b2=21.

So, the system of equations are,

a+b=7a2-b2=21

02

Step 2 Let us write the first equation as,

a=7-b.

Substitute the value of ain the second equation.

7-b2-b2=2172-14b+b2-b2=2149-14b=2114b=28b=2

03

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

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

So, the required numbers are,5,2.

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