Question

1 added to the product of two consecutive odd numbers gives 576. what are the numbers?​

Answer 1

Step-by-step explanation:

Given:-

1 added to the product of two consecutive odd numbers gives 576.

To find:-

What are the numbers?

Solution:-

We know that

The general form of an odd number = 2n+1

Let the two consecutive odd numbers be

2n+1 and 2n+3

Their product = (2n+1)(2n+3)

=>2n(2n+3)+1(2n+3)

=>4n^2 + 6n +2n +3

=>4n^2+8n+3

1 is added to the product of the consecutive odd numbers then it gives 576.

=>(4n^2+8n+3) +1= 576

=>4n^2+8n+4-576 = 0

=>4n^2+8n-572= 0

=>4(n^2+2n-143) = 0

=>n^2+2n-143 = 0/4

=> n^2+2n-143 = 0

=>n^2+13n-11n-143 = 0

=>n(n+13)-11(n+13)=0

=>(n+13)(n-11) = 0

=>n+13 = 0 or n-11 = 0

=>n = -13 or n=11

If n = -13 then 2n+1 = 2(-13)+1 = -26+1=-25

2n+3 =2(-13)+3 = -26+3 = -23

The numbers = -23 and -25

If n=11 then 2n+1 = 2(11)+1 = 22+1 = 23

2n+3 = 2(11)+3 = 22+3 = 25

The numbers = 23 and 25

Answer:-

The two consecutive odd numbers = 23 and 25

or -23 and -25

Check:-

If the numbers are -23 and -25 then

their product = -23×-25 = 575

If 1 is added to the product = 575+1 = 576

If the numbers are 23 and 25 then

Their product = 23×25 = 575

If 1 is added to the product = 575+1 = 576

Verified the given relations.