Question

find two consecutive positive odd numbers such that the sum of their squares is 113

Answer 1

let the two odd numbers be n , n+2

given

n²+(n+2)²=113

n²+n²+4+2(2)(n)=113

2n²+4n+4-113=0

2n²+4n-109=0

We get irrational values.

so check with trial and error.

3²+5²=9+25=34

5²+7²=25+49=74

7²+9²=49+81= 130

so we observe that sum of squares of two positive odd numbers cant be 113

it the sum of squares of odd numbers is130, then the numbers are 7,9

hope helped!