Question

The sum of the squares of two consecutive odd numbers is 394. Find the numbers​

Answer 1

Answer:

13 and 15 ..........................

Answer 2

Step-by-step explanation:

Given:-

The sum of the squares of two consecutive odd numbers is 394.

To find:-

Find the numbers

Solution:-

The general form of an odd is 2n+1

Let the two consecutive numbers be 2n+1 and 2n+3.

Their squares are (2n+1)² and (2n+3)²

Their sum =(2n+1)² +(2n+3)²

(a+b)²=a²+2ab+b²)

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

=>4n²+4n+1+4n²+12n+9

=>8n²+16n+10

According to the given problem

Their sum =394

=>8n²+16n+10=394

=>8n²+16n+10-394=0

=>8n²+16n-384=0

=>8(n²+2n-48)=0

=>n²+2n-48=0/8

=>n²+2n-48=0

=>n²+8n-6n-48=0

=>n(n+8)-6(n+8)=0

=>(n+8)(n-6)=0

=>n+8=0 or n-6=0

=>n=-8 or n=6

If n=-8 then 2n+1=>2(-8)+1=-16+1=-15

and 2n+3=2(-8)+3=-16+3=-13

If n=6 then 2n+1=2(6)+1=12+1=13

and 2n+3=2(6)+3=12+3=15

Answer:-

The required cosecutive odd numbers are 13 and 15

(If given they are positive)

Check:-

13²+15²=169+225=394